Phylogenetic diversity in other problems - GPTP 2021

Other fitness landscapes

Setup

library(ggplot2)
library(tidyverse)
library(knitr)
library(cowplot)
library(viridis)
library(RColorBrewer)
library(rstatix)
library(ggsignif)
library(Hmisc)
library(kableExtra)
source("https://gist.githubusercontent.com/benmarwick/2a1bb0133ff568cbe28d/raw/fb53bd97121f7f9ce947837ef1a4c65a73bffb3f/geom_flat_violin.R")
library(readr)
library(stringr)
library(ggpubr)
library(infotheo)
library(osfr)
library(scales)

These analyses were conducted in the following computing environment:

print(version)

##                _                           
## platform       x86_64-pc-linux-gnu         
## arch           x86_64                      
## os             linux-gnu                   
## system         x86_64, linux-gnu           
## status                                     
## major          4                           
## minor          0.4                         
## year           2021                        
## month          02                          
## day            15                          
## svn rev        80002                       
## language       R                           
## version.string R version 4.0.4 (2021-02-15)
## nickname       Lost Library Book

# Labeler for stats annotations
p_label <- function(p_value) {
  threshold = 0.0001
  if (p_value < threshold) {
    return(paste0("p < ", threshold))
  } else {
    return(paste0("p = ", p_value))
  }
}

# Significance threshold
alpha <- 0.05

####### misc #######
# Configure our default graphing theme
theme_set(theme_cowplot())

osf_retrieve_file("p79hx") %>% osf_download(conflicts = "skip")  # Download data from osf

## # A tibble: 1 x 4
##   name                   id                local_path               meta        
##   <chr>                  <chr>             <chr>                    <list>      
## 1 complex_fitness_lands… 612fe4d84e5ee501… ./complex_fitness_lands… <named list…

data_loc <- "complex_fitness_landscapes.csv"

data <- read_csv(data_loc, na=c("NONE", "NA", ""))

data <- data %>% 
  filter(N==20, generation %%10 == 0) %>%
  mutate(
  selection_name = as.factor(case_when(
    SELECTION == 0 ~ "Tournament",
    SELECTION == 1 ~ "Fitness sharing",
    SELECTION == 2 ~ "Lexicase",
    SELECTION == 3 ~ "Eco-EA",
    SELECTION == 4 ~ "Random",
  )), 
  problem_name = as.factor(case_when(
    PROBLEM == 0 ~ "NK Landscape",
    PROBLEM == 1 ~ "Count Odds",
    PROBLEM == 2 ~ "Real-valued optimization",
    PROBLEM == 3 ~ "Sorting network",
    PROBLEM == 4 ~ "Logic-9"    
  ))
)

data <- filter(data, generation <= 2000)
final_data <- filter(data, generation==max(data$generation))

Performance

Over time

ggplot(
    data,
    aes(
      x=generation,
      y=max_performance,
      color=selection_name,
      fill=selection_name
    )
  ) +
  stat_summary(geom="line", fun=mean) +
  stat_summary(
    geom="ribbon",
    fun.data="mean_cl_boot",
    fun.args=list(conf.int=0.95),
    alpha=0.2,
    linetype=0
  ) +
  scale_y_continuous(
    name="Average trait performance"
  ) +
  scale_x_continuous(
    name="Generation"
  ) +
  scale_color_discrete("Selection") + 
  scale_fill_discrete("Selection") +
  facet_wrap(~problem_name, scales="free")

Final

# Compute manual labels for geom_signif
stat.test <- final_data %>%
  wilcox_test(max_performance ~ selection_name) %>%
  adjust_pvalue(method = "bonferroni") %>%
  add_significance() %>%
  add_xy_position(x="selection_name",step.increase=1)
#stat.test$manual_position <- stat.test$y.position * .5
#stat.test$manual_position <- c(110, 1100, 170, 170, 130, 110)
stat.test$label <- mapply(p_label,stat.test$p.adj)

ggplot(
    final_data,
    aes(
      x=selection_name,
      y=max_performance,
      fill=selection_name
    )
  ) +
  geom_boxplot() +
  scale_y_continuous(
    name="Average trait performance"
  ) +
  scale_x_discrete(
    name="Selection"
  ) +
  scale_fill_discrete(
    name="Selection"
  ) +
  scale_color_discrete(
    name="Selection"
  ) + 
  theme(legend.position="none") +
  facet_wrap(~problem_name, scales="free")

stat.test %>%
  kbl() %>%
  kable_styling(
    bootstrap_options = c(
      "striped",
      "hover",
      "condensed",
      "responsive"
    )
  ) %>%
  scroll_box(width="600px")

.y.	group1	group2	n1	n2	statistic	p	p.adj	p.adj.signif	y.position	groups	xmin	xmax	label
max_performance	Eco-EA	Fitness sharing	240	240	28898.5	9.49e-01	1.00e+00	ns	102283.6	Eco-EA , Fitness sharing	1	2	p = 1
max_performance	Eco-EA	Lexicase	240	240	22536.0	3.25e-05	3.25e-04	***	135739.0	Eco-EA , Lexicase	1	3	p = 0.000325
max_performance	Eco-EA	Random	240	240	38664.0	0.00e+00	0.00e+00	****	169194.5	Eco-EA, Random	1	4	p < 1e-04
max_performance	Eco-EA	Tournament	240	240	28335.5	7.59e-01	1.00e+00	ns	202649.9	Eco-EA , Tournament	1	5	p = 1
max_performance	Fitness sharing	Lexicase	240	240	21248.5	7.00e-07	6.50e-06	****	236105.4	Fitness sharing, Lexicase	2	3	p < 1e-04
max_performance	Fitness sharing	Random	240	240	40208.0	0.00e+00	0.00e+00	****	269560.8	Fitness sharing, Random	2	4	p < 1e-04
max_performance	Fitness sharing	Tournament	240	240	26515.0	1.33e-01	1.00e+00	ns	303016.3	Fitness sharing, Tournament	2	5	p = 1
max_performance	Lexicase	Random	240	240	44119.5	0.00e+00	0.00e+00	****	336471.7	Lexicase, Random	3	4	p < 1e-04
max_performance	Lexicase	Tournament	240	240	35022.0	3.93e-05	3.93e-04	***	369927.2	Lexicase , Tournament	3	5	p = 0.000393
max_performance	Random	Tournament	240	240	17928.5	0.00e+00	0.00e+00	****	403382.6	Random , Tournament	4	5	p < 1e-04

Phylogenetic diversity

Relationship between different types of pylogenetic diversity

First, to get a big-picture overview, we make correlation matrices of all the different phylogenetic diversity metrics:

final_data %>% 
  transmute(MinPD=min_phenotype_pairwise_distance, 
            MeanPD=mean_phenotype_pairwise_distance, 
            MaxPD=max_phenotype_pairwise_distance, 
            VarPD=variance_phenotype_pairwise_distance, 
            MinED = min_phenotype_evolutionary_distinctiveness,
            MeanED= mean_phenotype_evolutionary_distinctiveness,
            MaxED=max_phenotype_evolutionary_distinctiveness,
            VarED=variance_phenotype_evolutionary_distinctiveness,
            PD=phenotype_current_phylogenetic_diversity,  # See Faith 1992
            MRCA=phenotype_mrca_depth,  # Phylogenetic depth of most recent common ancestor
            N=phenotype_num_taxa     # Number of taxonomically-distinct phenotypes
  ) %>%
  cor_mat() %>% 
  pull_lower_triangle() %>% 
  cor_plot()

However, these correlations may well vary by selection scheme and by problem, and even over time within a selection scheme and problem. Let’s take a look at some scatter plots.

ggplot(
    data %>% filter(generation==1000),
    aes(
        y=mean_phenotype_pairwise_distance,
        x=variance_phenotype_pairwise_distance,
        color=selection_name,
        fill=selection_name
    )
  ) +
  geom_point() +
  scale_x_continuous(
        breaks = breaks_extended(4)
  ) + 
  facet_wrap(
      ~selection_name*problem_name, ncol=4, scales="free"
  ) + 
  stat_smooth(
    method="lm"
  ) + 
  stat_cor(
    method="spearman", cor.coef.name = "rho", color="black"
  ) +
  theme(legend.position = "none")

ggplot(
    data %>% filter(generation==1000),
    aes(
        y=mean_phenotype_pairwise_distance,
        x=max_phenotype_pairwise_distance,
        color=selection_name,
        fill=selection_name
    )
  ) +
  geom_point() +
  scale_x_continuous(
        breaks = breaks_extended(4)
  ) + 
  facet_wrap(
      ~selection_name*problem_name, ncol=4, scales="free"
  ) + 
  stat_smooth(
    method="lm"
  ) + 
  stat_cor(
    method="spearman", cor.coef.name = "rho", color="black"
  ) +
  theme(legend.position = "none")

ggplot(
    data %>% filter(generation==1000),
    aes(
        y=variance_phenotype_pairwise_distance,
        x=max_phenotype_pairwise_distance,
        color=selection_name,
        fill=selection_name
    )
  ) +
  geom_point() +
  scale_x_continuous(
        breaks = breaks_extended(4)
  ) + 
  facet_wrap(
      ~selection_name*problem_name, ncol=4, scales="free"
  ) + 
  stat_smooth(
    method="lm"
  ) + 
  stat_cor(
    method="spearman", cor.coef.name = "rho", color="black"
  ) +
  theme(legend.position = "none")

ggplot(
    data %>% filter(generation==500),
    aes(
        y=mean_phenotype_pairwise_distance,
        x=variance_phenotype_pairwise_distance,
        color=selection_name,
        fill=selection_name
    )
  ) +
  geom_point() +
  scale_x_continuous(
        breaks = breaks_extended(4)
  ) + 
  facet_wrap(
      ~selection_name*problem_name, ncol=4, scales="free"
  ) + 
  stat_smooth(
    method="lm"
  ) + 
  stat_cor(
    method="spearman", cor.coef.name = "rho", color="black"
  ) +
  theme(legend.position = "none")

ggplot(
    data %>% filter(generation==500),
    aes(
        y=mean_phenotype_pairwise_distance,
        x=max_phenotype_pairwise_distance,
        color=selection_name,
        fill=selection_name
    )
  ) +
  geom_point() +
  scale_x_continuous(
        breaks = breaks_extended(4)
  ) + 
  facet_wrap(
      ~selection_name*problem_name, ncol=4, scales="free"
  ) + 
  stat_smooth(
    method="lm"
  ) + 
  stat_cor(
    method="spearman", cor.coef.name = "rho", color="black"
  ) +
  theme(legend.position = "none")

ggplot(
    data %>% filter(generation==1000),
    aes(
        y=variance_phenotype_pairwise_distance,
        x=max_phenotype_pairwise_distance,
        color=selection_name,
        fill=selection_name
    )
  ) +
  geom_point() +
  scale_x_continuous(
        breaks = breaks_extended(4)
  ) + 
  facet_wrap(
      ~selection_name*problem_name, ncol=4, scales="free"
  ) + 
  stat_smooth(
    method="lm"
  ) + 
  stat_cor(
    method="spearman", cor.coef.name = "rho", color="black"
  ) +
  theme(legend.position = "none")

ggplot(
    data %>% filter(generation==1000),
    aes(
        y=mean_phenotype_evolutionary_distinctiveness,
        x=variance_phenotype_evolutionary_distinctiveness,
        color=selection_name,
        fill=selection_name
    )
  ) +
  geom_point() +
  scale_x_continuous(
        breaks = breaks_extended(4)
  ) + 
  facet_wrap(
      ~selection_name*problem_name, ncol=4, scales="free"
  ) + 
  stat_smooth(
    method="lm"
  ) + 
  stat_cor(
    method="spearman", cor.coef.name = "rho", color="black"
  ) +
  theme(legend.position = "none")

ggplot(
    data %>% filter(generation==1000),
    aes(
        y=mean_phenotype_evolutionary_distinctiveness,
        x=max_phenotype_evolutionary_distinctiveness,
        color=selection_name,
        fill=selection_name
    )
  ) +
  geom_point() +
  scale_x_continuous(
        breaks = breaks_extended(4)
  ) + 
  facet_wrap(
      ~selection_name*problem_name, ncol=4, scales="free"
  ) + 
  stat_smooth(
    method="lm"
  ) + 
  stat_cor(
    method="spearman", cor.coef.name = "rho", color="black"
  ) +
  theme(legend.position = "none")

ggplot(
    data %>% filter(generation==1000),
    aes(
        y=mean_phenotype_evolutionary_distinctiveness,
        x=min_phenotype_evolutionary_distinctiveness,
        color=selection_name,
        fill=selection_name
    )
  ) +
  geom_point() +
  scale_x_continuous(
        breaks = breaks_extended(4)
  ) + 
  facet_wrap(
      ~selection_name*problem_name, ncol=4, scales="free"
  ) + 
  stat_smooth(
    method="lm"
  ) + 
  stat_cor(
    method="spearman", cor.coef.name = "rho", color="black"
  ) +
  theme(legend.position = "none")

ggplot(
    data %>% filter(generation==500),
    aes(
        y=mean_phenotype_evolutionary_distinctiveness,
        x=variance_phenotype_evolutionary_distinctiveness,
        color=selection_name,
        fill=selection_name
    )
  ) +
  geom_point() +
  scale_x_continuous(
        breaks = breaks_extended(4)
  ) + 
  facet_wrap(
      ~selection_name*problem_name, ncol=4, scales="free"
  ) + 
  stat_smooth(
    method="lm"
  ) + 
  stat_cor(
    method="spearman", cor.coef.name = "rho", color="black"
  ) +
  theme(legend.position = "none")

ggplot(
    data %>% filter(generation==500),
    aes(
        y=mean_phenotype_evolutionary_distinctiveness,
        x=max_phenotype_evolutionary_distinctiveness,
        color=selection_name,
        fill=selection_name
    )
  ) +
  geom_point() +
  scale_x_continuous(
        breaks = breaks_extended(4)
  ) + 
  facet_wrap(
      ~selection_name*problem_name, ncol=4, scales="free"
  ) + 
  stat_smooth(
    method="lm"
  ) + 
  stat_cor(
    method="spearman", cor.coef.name = "rho", color="black"
  ) +
  theme(legend.position = "none")

ggplot(
    data %>% filter(generation==500),
    aes(
        y=mean_phenotype_evolutionary_distinctiveness,
        x=min_phenotype_evolutionary_distinctiveness,
        color=selection_name,
        fill=selection_name
    )
  ) +
  geom_point() +
  scale_x_continuous(
        breaks = breaks_extended(4)
  ) + 
  facet_wrap(
      ~selection_name*problem_name, ncol=4, scales="free"
  ) + 
  stat_smooth(
    method="lm"
  ) + 
  stat_cor(
    method="spearman", cor.coef.name = "rho", color="black"
  ) +
  theme(legend.position = "none")

Over time

ggplot(
    data,
    aes(
      x=generation,
      y=mean_phenotype_pairwise_distance,
      color=selection_name,
      fill=selection_name
    )
  ) +
  stat_summary(geom="line", fun=mean) +
  stat_summary(
    geom="ribbon",
    fun.data="mean_cl_boot",
    fun.args=list(conf.int=0.95),
    alpha=0.2,
    linetype=0
  ) +
  scale_y_log10(
    name="Mean pairwise distance"
  ) +
  scale_x_continuous(
    name="Generation"
  ) +
  scale_color_discrete("Selection") +
  scale_fill_discrete("Selection") +
  facet_wrap(~problem_name, scales = "free")

Final

# Compute manual labels for geom_signif
stat.test <- final_data %>%
  wilcox_test(mean_phenotype_pairwise_distance ~ selection_name) %>%
  adjust_pvalue(method = "bonferroni") %>%
  add_significance() %>%
  add_xy_position(x="selection_name",step.increase=1)
#stat.test$manual_position <- stat.test$y.position * .5
#stat.test$manual_position <- c(110, 150, 170, 170, 130, 110)
stat.test$label <- mapply(p_label,stat.test$p.adj)

ggplot(
    final_data,
    aes(
      x=selection_name,
      y=mean_phenotype_pairwise_distance,
      fill=selection_name
    )
  ) +
  geom_boxplot() +
  scale_y_log10(
    name="Mean pairwise distance"
  ) +
  scale_x_discrete(
    name="Selection"
  ) +
  scale_fill_discrete(
    name="Selection"
  ) +
  scale_color_discrete(
    name="Selection"
  ) + 
  theme(legend.position = "none") +
    facet_wrap(~problem_name, scales = "free")

stat.test %>%
  kbl() %>%
  kable_styling(
    bootstrap_options = c(
      "striped",
      "hover",
      "condensed",
      "responsive"
    )
  ) %>%
  scroll_box(width="600px")

.y.	group1	group2	n1	n2	statistic	p	p.adj	p.adj.signif	y.position	groups	xmin	xmax	label
mean_phenotype_pairwise_distance	Eco-EA	Fitness sharing	240	240	2486.0	0.00e+00	0.00e+00	****	2900.227	Eco-EA , Fitness sharing	1	2	p < 1e-04
mean_phenotype_pairwise_distance	Eco-EA	Lexicase	240	240	23590.0	6.07e-04	6.07e-03	**	4498.579	Eco-EA , Lexicase	1	3	p = 0.00607
mean_phenotype_pairwise_distance	Eco-EA	Random	240	240	8274.0	0.00e+00	0.00e+00	****	6096.931	Eco-EA, Random	1	4	p < 1e-04
mean_phenotype_pairwise_distance	Eco-EA	Tournament	240	240	43940.0	0.00e+00	0.00e+00	****	7695.284	Eco-EA , Tournament	1	5	p < 1e-04
mean_phenotype_pairwise_distance	Fitness sharing	Lexicase	240	240	35067.0	3.72e-05	3.72e-04	***	9293.636	Fitness sharing, Lexicase	2	3	p = 0.000372
mean_phenotype_pairwise_distance	Fitness sharing	Random	240	240	37442.0	0.00e+00	1.00e-07	****	10891.988	Fitness sharing, Random	2	4	p < 1e-04
mean_phenotype_pairwise_distance	Fitness sharing	Tournament	240	240	57033.0	0.00e+00	0.00e+00	****	12490.340	Fitness sharing, Tournament	2	5	p < 1e-04
mean_phenotype_pairwise_distance	Lexicase	Random	240	240	26406.0	1.15e-01	1.00e+00	ns	14088.693	Lexicase, Random	3	4	p = 1
mean_phenotype_pairwise_distance	Lexicase	Tournament	240	240	36500.5	4.00e-07	4.00e-06	****	15687.045	Lexicase , Tournament	3	5	p < 1e-04
mean_phenotype_pairwise_distance	Random	Tournament	240	240	55686.0	0.00e+00	0.00e+00	****	17285.397	Random , Tournament	4	5	p < 1e-04

Phenotypic diversity

Relationship between different types of phenotypic diversity

First, we should assess the extent to which different metrics of phenotypic diversity are capturing different information.

ggplot(
    data %>% filter(generation==1000),
    aes(
        y=phenotype_diversity,
        x=phenotype_num_taxa,
        color=selection_name,
        fill=selection_name
    )
  ) +
  geom_point() +
    scale_y_continuous(
        name="Phenotypic shannon diversity"
  ) +
  scale_x_continuous(
        name="Phenotypic richness",
        breaks = breaks_extended(4)
  ) + 
  facet_wrap(
      ~selection_name*problem_name, ncol=4, scales="free"
  ) + 
  stat_smooth(
    method="lm"
  ) + 
  stat_cor(
    method="spearman", cor.coef.name = "rho", color="black"
  ) +
  theme(legend.position = "none")

Over time

ggplot(
    data,
    aes(
      x=generation,
      y=phenotype_num_taxa,
      color=selection_name,
      fill=selection_name
    )
  ) +
  stat_summary(geom="line", fun=mean) +
  stat_summary(
    geom="ribbon",
    fun.data="mean_cl_boot",
    fun.args=list(conf.int=0.95),
    alpha=0.2,
    linetype=0
  ) +
  scale_y_continuous(
    name="Phenotypic richness"
  ) +
  scale_x_continuous(
    name="Generation"
  ) +
  scale_color_discrete("Selection") + 
  scale_fill_discrete("Selection") +
  facet_wrap(~problem_name, scales = "free")

Final

# Compute manual labels for geom_signif
stat.test <- final_data %>%
  wilcox_test(phenotype_num_taxa ~ selection_name) %>%
  adjust_pvalue(method = "bonferroni") %>%
  add_significance() %>%
  add_xy_position(x="selection_name",step.increase=1)
#stat.test$manual_position <- stat.test$y.position * .5
#stat.test$manual_position <- c(110, 150, 170, 170, 130, 110)
stat.test$label <- mapply(p_label,stat.test$p.adj)

ggplot(
    final_data,
    aes(
      x=selection_name,
      y=phenotype_num_taxa,
      fill=selection_name
    )
  ) +
  geom_boxplot() +
  scale_y_continuous(
    name="Phenotypic Richness"
  ) +
  scale_x_discrete(
    name="Selection"
  ) +
  scale_fill_discrete(
    name="Selection"
  ) +
  scale_color_discrete(
    name="Selection"
  ) +
  theme(legend.position = "none") +
  facet_wrap(~problem_name, scales = "free")

stat.test %>%
  kbl() %>%
  kable_styling(
    bootstrap_options = c(
      "striped",
      "hover",
      "condensed",
      "responsive"
    )
  ) %>%
  scroll_box(width="600px")

.y.	group1	group2	n1	n2	statistic	p	p.adj	p.adj.signif	y.position	groups	xmin	xmax	label
phenotype_num_taxa	Eco-EA	Fitness sharing	240	240	3513.5	0.00000	0.0000	****	1580.000	Eco-EA , Fitness sharing	1	2	p < 1e-04
phenotype_num_taxa	Eco-EA	Lexicase	240	240	17757.5	0.00000	0.0000	****	2224.444	Eco-EA , Lexicase	1	3	p < 1e-04
phenotype_num_taxa	Eco-EA	Random	240	240	38186.0	0.00000	0.0000	****	2868.889	Eco-EA, Random	1	4	p < 1e-04
phenotype_num_taxa	Eco-EA	Tournament	240	240	30723.0	0.20600	1.0000	ns	3513.333	Eco-EA , Tournament	1	5	p = 1
phenotype_num_taxa	Fitness sharing	Lexicase	240	240	39523.5	0.00000	0.0000	****	4157.778	Fitness sharing, Lexicase	2	3	p < 1e-04
phenotype_num_taxa	Fitness sharing	Random	240	240	56742.5	0.00000	0.0000	****	4802.222	Fitness sharing, Random	2	4	p < 1e-04
phenotype_num_taxa	Fitness sharing	Tournament	240	240	49804.5	0.00000	0.0000	****	5446.667	Fitness sharing, Tournament	2	5	p < 1e-04
phenotype_num_taxa	Lexicase	Random	240	240	46856.0	0.00000	0.0000	****	6091.111	Lexicase, Random	3	4	p < 1e-04
phenotype_num_taxa	Lexicase	Tournament	240	240	41709.5	0.00000	0.0000	****	6735.556	Lexicase , Tournament	3	5	p < 1e-04
phenotype_num_taxa	Random	Tournament	240	240	23410.5	0.00039	0.0039	**	7380.000	Random , Tournament	4	5	p = 0.0039

Relationship between phenotypic and phylogenetic diversity

ggplot(
    final_data,
    aes(
        y=phenotype_num_taxa,
        x=mean_phenotype_pairwise_distance,
        color=selection_name,
        fill=selection_name
    )
  ) +
  geom_point() +
    scale_y_continuous(
        name="Phenotypic richness"
  ) +
  scale_x_continuous(
        name="Mean pairwise distance"
  ) + 
  facet_wrap(
      ~selection_name*problem_name, ncol=4, scales="free"
  ) + 
  stat_smooth(
    method="lm"
  ) + 
  stat_cor(
    method="spearman", cor.coef.name = "rho", color="black"
  ) +
  theme(legend.position = "none")

Relationship between diversity and success

Earlier in run

ggplot(
    data %>% filter(generation==500),
    aes(
        y=max_performance,
        x=mean_phenotype_pairwise_distance,
        color=selection_name,
        fill=selection_name
    )
  ) +
  geom_point() +
    scale_y_continuous(
        name="Average trait performance"
  ) +
  scale_x_continuous(
        name="Mean pairwise distance"
  ) + 
  facet_wrap(
      ~selection_name*problem_name, ncol=4, scales="free"
  ) + 
  stat_smooth(
    method="lm"
  ) + 
  stat_cor(
    method="spearman", cor.coef.name = "rho", color="black"
  ) +
  theme(legend.position = "none")

ggplot(
    data %>% filter(generation==500),
    aes(
        y=max_performance,
        x=phenotype_num_taxa,
        color=selection_name,
        fill=selection_name
    )
  ) +
  geom_point() +
    scale_y_continuous(
        name="Average trait performance"
  ) +
  scale_x_continuous(
        name="Phenotypic richness"
  ) + 
  facet_wrap(
      ~selection_name*problem_name, ncol=4, scales="free"
  ) + 
  stat_smooth(
    method="lm"
  ) + 
  stat_cor(
    method="spearman", cor.coef.name = "rho", color="black"
  ) +
  theme(legend.position = "none")

phylogney_vs_performance <- ggplot(
    data %>% filter(generation==1000),
    aes(
        y=max_performance,
        x=mean_phenotype_pairwise_distance,
        color=selection_name,
        fill=selection_name
    )
  ) +
  geom_point() +
    scale_y_continuous(
        name="Average trait performance"
  ) +
  scale_x_continuous(
        name="Mean pairwise distance"
  ) + 
  facet_wrap(
      ~selection_name*problem_name, ncol=4, scales="free"
  ) + 
  stat_smooth(
    method="lm"
  ) + 
  stat_cor(
    method="spearman", cor.coef.name = "rho", color="black"
  ) +
  theme(legend.position = "none")
  
phylogney_vs_performance

ggplot(
    data %>% filter(generation==1000),
    aes(
        y=max_performance,
        x=phenotype_num_taxa,
        color=selection_name,
        fill=selection_name
    )
  ) +
  geom_point() +
    scale_y_continuous(
        name="Average trait performance"
  ) +
  scale_x_continuous(
        name="Phenotypic richness"
  ) + 
  facet_wrap(
      ~selection_name*problem_name, ncol=4, scales="free"
  ) + 
  stat_smooth(
    method="lm"
  ) + 
  stat_cor(
    method="spearman", cor.coef.name = "rho", color="black"
  ) +
  theme(legend.position = "none")

End of run

ggplot(
    final_data,
    aes(
        y=max_performance,
        x=mean_phenotype_pairwise_distance,
        color=selection_name,
        fill=selection_name
    )
  ) +
  geom_point() +
    scale_y_continuous(
        name="Average trait performance"
  ) +
  scale_x_continuous(
        name="Mean pairwise distance"
  ) + 
  facet_wrap(
      ~selection_name*problem_name, ncol=4, scales="free"
  ) + 
  stat_smooth(
    method="lm"
  ) + 
  stat_cor(
    method="spearman", cor.coef.name = "rho", color="black"
  ) +
  theme(legend.position = "none")

ggplot(
    final_data,
    aes(
        y=max_performance,
        x=phenotype_num_taxa,
        color=selection_name,
        fill=selection_name
    )
  ) +
  geom_point() +
    scale_y_continuous(
        name="Average trait performance"
  ) +
  scale_x_continuous(
        name="Phenotypic richness"
  ) + 
  facet_wrap(
      ~selection_name*problem_name, ncol=4, scales="free"
  ) + 
  stat_smooth(
    method="lm"
  ) + 
  stat_cor(
    method="spearman", cor.coef.name = "rho", color="black"
  ) +
  theme(legend.position = "none")

Causality analysis

Setup

First let’s define a function we’ll use to calculate and output significance and effect size for these results:

transfer_entropy_stats <- function(res) {
  stat.test <- res %>%
    group_by(selection_name, problem_name, offset) %>%
    filter(max(value) > 0) %>% # Sorting networks have some values of 0, which won't work for Wilcox test
    wilcox_test(value ~ Type) %>%
    adjust_pvalue(method = "bonferroni") %>%
    add_significance() 
  stat.test$label <- mapply(p_label,stat.test$p.adj)
  
  # Calculate effect sizes for these differences
  effect_sizes <- res %>%
    group_by(selection_name, problem_name, offset) %>%
    filter(max(value) > 0) %>%
    wilcox_effsize(value ~ Type)
  
  stat.test$effsize <- effect_sizes$effsize
  stat.test$magnitude <- effect_sizes$magnitude
  
  stat.test %>%
    kbl() %>%
    kable_styling(
      bootstrap_options = c(
        "striped",
        "hover",
        "condensed",
        "responsive"
      )
    ) %>%
    scroll_box(width="800px")
}

Transfer entropy from diversity to fitness

Max pairwise distance vs. phenotypic richness

res <- data %>% group_by(SEED, selection_name, problem_name) %>%
summarise(
  fit_phylo_10 = condinformation(discretize(max_performance), discretize(lag(max_phenotype_pairwise_distance, 1)), discretize(lag(max_performance, 1))),
  fit_phylo_100 = condinformation(discretize(max_performance), discretize(lag(max_phenotype_pairwise_distance, 10)), discretize(lag(max_performance, 10))),
  fit_phylo_1000 = condinformation(discretize(max_performance), discretize(lag(max_phenotype_pairwise_distance, 100)), discretize(lag(max_performance, 100))),
    fit_pheno_10 = condinformation(discretize(max_performance), discretize(lag(phenotype_num_taxa, 1)), discretize(lag(max_performance, 1))),
      fit_pheno_100 = condinformation(discretize(max_performance), discretize(lag(phenotype_num_taxa, 10)), discretize(lag(max_performance, 10))),
      fit_pheno_1000 = condinformation(discretize(max_performance), discretize(lag(phenotype_num_taxa, 100)), discretize(lag(max_performance, 100)))
      )

res <- res %>% pivot_longer(cols=contains("o_10"))
res$offset <- str_extract(res$name, "[:digit:]*$")
res$Type <- case_when(str_detect(res$name, "phylo") ~ "Phylogenetic", TRUE ~ "Phenotypic")

ggplot(
  res %>% filter(str_detect(name, "fit_ph*")), 
  aes(
    x=as.factor(offset), 
    y=value, 
    color=Type
    )
  ) + 
  geom_boxplot() + 
  facet_wrap(~selection_name*problem_name, ncol=4) + 
  scale_x_discrete("Lag") + 
  scale_y_continuous("Transfer Entropy") + 
  scale_color_discrete("") + 
  theme(legend.position = "bottom")

# Determine which conditions are significantly different from each other
transfer_entropy_stats(res)

selection_name	problem_name	offset	.y.	group1	group2	n1	n2	statistic	p	p.adj	p.adj.signif	label	effsize	magnitude
Eco-EA	Count Odds	10	value	Phenotypic	Phylogenetic	60	60	1358.0	2.05e-02	1.0000000	ns	p = 1	0.2117768	small
Eco-EA	Count Odds	100	value	Phenotypic	Phylogenetic	60	60	739.0	0.00e+00	0.0000015	****	p < 1e-04	0.5083601	large
Eco-EA	Count Odds	1000	value	Phenotypic	Phylogenetic	60	60	1054.0	9.12e-05	0.0053808	**	p = 0.0053808	0.3574394	moderate
Eco-EA	Logic-9	10	value	Phenotypic	Phylogenetic	60	60	1771.0	8.81e-01	1.0000000	ns	p = 1	0.0138951	small
Eco-EA	Logic-9	100	value	Phenotypic	Phylogenetic	60	60	1769.0	8.73e-01	1.0000000	ns	p = 1	0.0148534	small
Eco-EA	Logic-9	1000	value	Phenotypic	Phylogenetic	60	60	2028.0	2.30e-01	1.0000000	ns	p = 1	0.1097388	small
Eco-EA	NK Landscape	10	value	Phenotypic	Phylogenetic	60	60	1576.5	2.42e-01	1.0000000	ns	p = 1	0.1070864	small
Eco-EA	NK Landscape	100	value	Phenotypic	Phylogenetic	60	60	1536.5	1.67e-01	1.0000000	ns	p = 1	0.1262518	small
Eco-EA	NK Landscape	1000	value	Phenotypic	Phylogenetic	60	60	1788.0	9.52e-01	1.0000000	ns	p = 1	0.0057497	small
Eco-EA	Sorting network	10	value	Phenotypic	Phylogenetic	60	60	2070.0	1.57e-01	1.0000000	ns	p = 1	0.1295248	small
Eco-EA	Sorting network	100	value	Phenotypic	Phylogenetic	60	60	1838.0	8.44e-01	1.0000000	ns	p = 1	0.0182073	small
Eco-EA	Sorting network	1000	value	Phenotypic	Phylogenetic	60	60	1800.0	1.00e+00	1.0000000	ns	p = 1	0.0000000	small
Fitness sharing	Count Odds	10	value	Phenotypic	Phylogenetic	60	60	1631.0	3.76e-01	1.0000000	ns	p = 1	0.0809735	small
Fitness sharing	Count Odds	100	value	Phenotypic	Phylogenetic	60	60	1257.0	4.41e-03	0.2601900	ns	p = 0.26019	0.2601692	small
Fitness sharing	Count Odds	1000	value	Phenotypic	Phylogenetic	60	60	1501.0	1.17e-01	1.0000000	ns	p = 1	0.1432608	small
Fitness sharing	Logic-9	10	value	Phenotypic	Phylogenetic	60	60	1511.0	1.30e-01	1.0000000	ns	p = 1	0.1384718	small
Fitness sharing	Logic-9	100	value	Phenotypic	Phylogenetic	60	60	1309.0	1.00e-02	0.5900000	ns	p = 0.59	0.2352584	small
Fitness sharing	Logic-9	1000	value	Phenotypic	Phylogenetic	60	60	1629.5	3.71e-01	1.0000000	ns	p = 1	0.0819116	small
Fitness sharing	NK Landscape	10	value	Phenotypic	Phylogenetic	60	60	1196.0	1.54e-03	0.0908600	ns	p = 0.09086	0.2893963	small
Fitness sharing	NK Landscape	100	value	Phenotypic	Phylogenetic	60	60	562.0	0.00e+00	0.0000000	****	p < 1e-04	0.5931666	large
Fitness sharing	NK Landscape	1000	value	Phenotypic	Phylogenetic	60	60	477.0	0.00e+00	0.0000000	****	p < 1e-04	0.6338929	large
Fitness sharing	Sorting network	10	value	Phenotypic	Phylogenetic	60	60	820.0	3.00e-07	0.0000161	****	p < 1e-04	0.4695503	moderate
Fitness sharing	Sorting network	100	value	Phenotypic	Phylogenetic	60	60	366.0	0.00e+00	0.0000000	****	p < 1e-04	0.6870767	large
Fitness sharing	Sorting network	1000	value	Phenotypic	Phylogenetic	60	60	1349.0	1.81e-02	1.0000000	ns	p = 1	0.2160890	small
Lexicase	Count Odds	10	value	Phenotypic	Phylogenetic	60	60	1579.0	2.47e-01	1.0000000	ns	p = 1	0.1058884	small
Lexicase	Count Odds	100	value	Phenotypic	Phylogenetic	60	60	285.0	0.00e+00	0.0000000	****	p < 1e-04	0.7258865	large
Lexicase	Count Odds	1000	value	Phenotypic	Phylogenetic	60	60	694.0	0.00e+00	0.0000004	****	p < 1e-04	0.5299211	large
Lexicase	Logic-9	10	value	Phenotypic	Phylogenetic	60	60	1963.5	3.92e-01	1.0000000	ns	p = 1	0.0783384	small
Lexicase	Logic-9	100	value	Phenotypic	Phylogenetic	60	60	1490.5	1.05e-01	1.0000000	ns	p = 1	0.1482919	small
Lexicase	Logic-9	1000	value	Phenotypic	Phylogenetic	60	60	1830.0	8.77e-01	1.0000000	ns	p = 1	0.0144184	small
Lexicase	NK Landscape	10	value	Phenotypic	Phylogenetic	60	60	1752.0	8.02e-01	1.0000000	ns	p = 1	0.0231457	small
Lexicase	NK Landscape	100	value	Phenotypic	Phylogenetic	60	60	1311.0	9.87e-03	0.5823300	ns	p = 0.58233	0.2357967	small
Lexicase	NK Landscape	1000	value	Phenotypic	Phylogenetic	60	60	1064.0	1.02e-04	0.0060180	**	p = 0.006018	0.3549006	moderate
Lexicase	Sorting network	10	value	Phenotypic	Phylogenetic	60	60	1814.0	9.27e-01	1.0000000	ns	p = 1	0.0086195	small
Lexicase	Sorting network	100	value	Phenotypic	Phylogenetic	60	60	1798.5	9.95e-01	1.0000000	ns	p = 1	0.0009235	small
Random	Count Odds	10	value	Phenotypic	Phylogenetic	60	60	1699.0	5.98e-01	1.0000000	ns	p = 1	0.0483924	small
Random	Count Odds	100	value	Phenotypic	Phylogenetic	60	60	1700.0	6.02e-01	1.0000000	ns	p = 1	0.0479133	small
Random	Count Odds	1000	value	Phenotypic	Phylogenetic	60	60	921.0	4.00e-06	0.0002366	***	p = 0.00023659	0.4211579	moderate
Random	Logic-9	10	value	Phenotypic	Phylogenetic	60	60	1924.5	4.62e-01	1.0000000	ns	p = 1	0.0673727	small
Random	Logic-9	100	value	Phenotypic	Phylogenetic	60	60	1807.0	9.69e-01	1.0000000	ns	p = 1	0.0037879	small
Random	Logic-9	1000	value	Phenotypic	Phylogenetic	60	60	1775.0	8.62e-01	1.0000000	ns	p = 1	0.0161606	small
Random	NK Landscape	10	value	Phenotypic	Phylogenetic	60	60	1150.0	6.52e-04	0.0384680		p = 0.038468	0.3114364	moderate
Random	NK Landscape	100	value	Phenotypic	Phylogenetic	60	60	629.0	0.00e+00	0.0000000	****	p < 1e-04	0.5610647	large
Random	NK Landscape	1000	value	Phenotypic	Phylogenetic	60	60	524.0	0.00e+00	0.0000000	****	p < 1e-04	0.6113737	large
Random	Sorting network	10	value	Phenotypic	Phylogenetic	60	60	1862.0	7.47e-01	1.0000000	ns	p = 1	0.0297062	small
Random	Sorting network	100	value	Phenotypic	Phylogenetic	60	60	990.0	2.15e-05	0.0012685	**	p = 0.0012685	0.3880977	moderate
Random	Sorting network	1000	value	Phenotypic	Phylogenetic	60	60	839.0	5.00e-07	0.0000273	****	p < 1e-04	0.4604468	moderate
Tournament	Count Odds	10	value	Phenotypic	Phylogenetic	60	60	1577.0	2.43e-01	1.0000000	ns	p = 1	0.1068467	small
Tournament	Count Odds	100	value	Phenotypic	Phylogenetic	60	60	1441.0	5.99e-02	1.0000000	ns	p = 1	0.1720087	small
Tournament	Count Odds	1000	value	Phenotypic	Phylogenetic	60	60	1573.0	2.34e-01	1.0000000	ns	p = 1	0.1087738	small
Tournament	Logic-9	10	value	Phenotypic	Phylogenetic	60	60	1956.0	4.14e-01	1.0000000	ns	p = 1	0.0747460	small
Tournament	Logic-9	100	value	Phenotypic	Phylogenetic	60	60	1978.0	3.52e-01	1.0000000	ns	p = 1	0.0852872	small
Tournament	Logic-9	1000	value	Phenotypic	Phylogenetic	60	60	2040.5	2.02e-01	1.0000000	ns	p = 1	0.1168182	small
Tournament	NK Landscape	10	value	Phenotypic	Phylogenetic	60	60	1802.0	9.89e-01	1.0000000	ns	p = 1	0.0016220	small
Tournament	NK Landscape	100	value	Phenotypic	Phylogenetic	60	60	1790.0	9.33e-01	1.0000000	ns	p = 1	0.0081098	small
Tournament	NK Landscape	1000	value	Phenotypic	Phylogenetic	60	60	1792.0	9.47e-01	1.0000000	ns	p = 1	0.0064879	small
Tournament	Sorting network	10	value	Phenotypic	Phylogenetic	60	60	1964.0	3.91e-01	1.0000000	ns	p = 1	0.0785827	small
Tournament	Sorting network	100	value	Phenotypic	Phylogenetic	60	60	1330.0	1.37e-02	0.8083000	ns	p = 0.8083	0.2251925	small
Tournament	Sorting network	1000	value	Phenotypic	Phylogenetic	60	60	1816.5	9.29e-01	1.0000000	ns	p = 1	0.0083936	small

Mean pairwise distance vs. phenotypic richness

res <- data %>% group_by(SEED, selection_name, problem_name) %>%
summarise(
  fit_phylo_10 = condinformation(discretize(max_performance), discretize(lag(mean_phenotype_pairwise_distance, 1)), discretize(lag(max_performance, 1))),
  fit_phylo_100 = condinformation(discretize(max_performance), discretize(lag(mean_phenotype_pairwise_distance, 10)), discretize(lag(max_performance, 10))),
  fit_phylo_1000 = condinformation(discretize(max_performance), discretize(lag(mean_phenotype_pairwise_distance, 100)), discretize(lag(max_performance, 100))),
    fit_pheno_10 = condinformation(discretize(max_performance), discretize(lag(phenotype_num_taxa, 1)), discretize(lag(max_performance, 1))),
      fit_pheno_100 = condinformation(discretize(max_performance), discretize(lag(phenotype_num_taxa, 10)), discretize(lag(max_performance, 10))),
      fit_pheno_1000 = condinformation(discretize(max_performance), discretize(lag(phenotype_num_taxa, 100)), discretize(lag(max_performance, 100)))
      )

res <- res %>% pivot_longer(cols=contains("o_10"))
res$offset <- str_extract(res$name, "[:digit:]*$")
res$Type <- case_when(str_detect(res$name, "phylo") ~ "Phylogenetic", TRUE ~ "Phenotypic")

ggplot(
  res %>% filter(str_detect(name, "fit_ph*")), 
  aes(
    x=as.factor(offset), 
    y=value, 
    color=Type
    )
  ) + 
  geom_boxplot() + 
  facet_wrap(~selection_name*problem_name, ncol=4) + 
  scale_x_discrete("Lag") + 
  scale_y_continuous("Transfer Entropy") + 
  scale_color_discrete("") + 
  theme(legend.position = "bottom")

# Determine which conditions are significantly different from each other
transfer_entropy_stats(res)

selection_name	problem_name	offset	.y.	group1	group2	n1	n2	statistic	p	p.adj	p.adj.signif	label	effsize	magnitude
Eco-EA	Count Odds	10	value	Phenotypic	Phylogenetic	60	60	1623.0	3.54e-01	1.0000000	ns	p = 1	0.0848065	small
Eco-EA	Count Odds	100	value	Phenotypic	Phylogenetic	60	60	1031.0	5.49e-05	0.0032391	**	p = 0.0032391	0.3684533	moderate
Eco-EA	Count Odds	1000	value	Phenotypic	Phylogenetic	60	60	1304.0	9.30e-03	0.5487000	ns	p = 0.5487	0.2376541	small
Eco-EA	Logic-9	10	value	Phenotypic	Phylogenetic	60	60	1770.0	8.77e-01	1.0000000	ns	p = 1	0.0143742	small
Eco-EA	Logic-9	100	value	Phenotypic	Phylogenetic	60	60	1713.0	6.50e-01	1.0000000	ns	p = 1	0.0416853	small
Eco-EA	Logic-9	1000	value	Phenotypic	Phylogenetic	60	60	1688.0	5.57e-01	1.0000000	ns	p = 1	0.0538785	small
Eco-EA	NK Landscape	10	value	Phenotypic	Phylogenetic	60	60	1484.5	9.83e-02	1.0000000	ns	p = 1	0.1511667	small
Eco-EA	NK Landscape	100	value	Phenotypic	Phylogenetic	60	60	1584.5	2.59e-01	1.0000000	ns	p = 1	0.1032533	small
Eco-EA	NK Landscape	1000	value	Phenotypic	Phylogenetic	60	60	1782.0	9.27e-01	1.0000000	ns	p = 1	0.0086245	small
Eco-EA	Sorting network	10	value	Phenotypic	Phylogenetic	60	60	2062.5	1.69e-01	1.0000000	ns	p = 1	0.1259317	small
Eco-EA	Sorting network	100	value	Phenotypic	Phylogenetic	60	60	1936.0	4.77e-01	1.0000000	ns	p = 1	0.0651642	small
Eco-EA	Sorting network	1000	value	Phenotypic	Phylogenetic	60	60	1799.0	9.93e-01	1.0000000	ns	p = 1	0.0015407	small
Fitness sharing	Count Odds	10	value	Phenotypic	Phylogenetic	60	60	1674.0	5.10e-01	1.0000000	ns	p = 1	0.0603708	small
Fitness sharing	Count Odds	100	value	Phenotypic	Phylogenetic	60	60	1252.0	4.06e-03	0.2395400	ns	p = 0.23954	0.2625649	small
Fitness sharing	Count Odds	1000	value	Phenotypic	Phylogenetic	60	60	1611.0	3.22e-01	1.0000000	ns	p = 1	0.0905561	small
Fitness sharing	Logic-9	10	value	Phenotypic	Phylogenetic	60	60	1491.0	1.05e-01	1.0000000	ns	p = 1	0.1480547	small
Fitness sharing	Logic-9	100	value	Phenotypic	Phylogenetic	60	60	1260.0	4.63e-03	0.2731700	ns	p = 0.27317	0.2587363	small
Fitness sharing	Logic-9	1000	value	Phenotypic	Phylogenetic	60	60	1520.0	1.41e-01	1.0000000	ns	p = 1	0.1345174	small
Fitness sharing	NK Landscape	10	value	Phenotypic	Phylogenetic	60	60	1285.0	6.93e-03	0.4088700	ns	p = 0.40887	0.2467535	small
Fitness sharing	NK Landscape	100	value	Phenotypic	Phylogenetic	60	60	683.0	0.00e+00	0.0000003	****	p < 1e-04	0.5351915	large
Fitness sharing	NK Landscape	1000	value	Phenotypic	Phylogenetic	60	60	697.0	0.00e+00	0.0000004	****	p < 1e-04	0.5284837	large
Fitness sharing	Sorting network	10	value	Phenotypic	Phylogenetic	60	60	905.0	2.70e-06	0.0001575	***	p = 0.00015753	0.4288240	moderate
Fitness sharing	Sorting network	100	value	Phenotypic	Phylogenetic	60	60	361.0	0.00e+00	0.0000000	****	p < 1e-04	0.6894724	large
Fitness sharing	Sorting network	1000	value	Phenotypic	Phylogenetic	60	60	1043.0	7.17e-05	0.0042303	**	p = 0.0042303	0.3627037	moderate
Lexicase	Count Odds	10	value	Phenotypic	Phylogenetic	60	60	1491.0	1.05e-01	1.0000000	ns	p = 1	0.1480521	small
Lexicase	Count Odds	100	value	Phenotypic	Phylogenetic	60	60	367.0	0.00e+00	0.0000000	****	p < 1e-04	0.6865976	large
Lexicase	Count Odds	1000	value	Phenotypic	Phylogenetic	60	60	870.0	1.10e-06	0.0000631	****	p < 1e-04	0.4455937	moderate
Lexicase	Logic-9	10	value	Phenotypic	Phylogenetic	60	60	1785.5	9.41e-01	1.0000000	ns	p = 1	0.0069474	small
Lexicase	Logic-9	100	value	Phenotypic	Phylogenetic	60	60	1461.5	7.61e-02	1.0000000	ns	p = 1	0.1621868	small
Lexicase	Logic-9	1000	value	Phenotypic	Phylogenetic	60	60	1600.0	2.94e-01	1.0000000	ns	p = 1	0.0961228	small
Lexicase	NK Landscape	10	value	Phenotypic	Phylogenetic	60	60	1742.0	7.61e-01	1.0000000	ns	p = 1	0.0279677	small
Lexicase	NK Landscape	100	value	Phenotypic	Phylogenetic	60	60	1342.0	1.57e-02	0.9263000	ns	p = 0.9263	0.2208485	small
Lexicase	NK Landscape	1000	value	Phenotypic	Phylogenetic	60	60	1034.0	5.26e-05	0.0031034	**	p = 0.0031034	0.3693667	moderate
Lexicase	Sorting network	10	value	Phenotypic	Phylogenetic	60	60	1831.0	8.37e-01	1.0000000	ns	p = 1	0.0190860	small
Lexicase	Sorting network	100	value	Phenotypic	Phylogenetic	60	60	1814.0	9.27e-01	1.0000000	ns	p = 1	0.0086195	small
Random	Count Odds	10	value	Phenotypic	Phylogenetic	60	60	1753.0	8.07e-01	1.0000000	ns	p = 1	0.0225193	small
Random	Count Odds	100	value	Phenotypic	Phylogenetic	60	60	1963.0	3.94e-01	1.0000000	ns	p = 1	0.0780987	small
Random	Count Odds	1000	value	Phenotypic	Phylogenetic	60	60	1176.0	1.07e-03	0.0631300	ns	p = 0.06313	0.2989790	small
Random	Logic-9	10	value	Phenotypic	Phylogenetic	60	60	1787.5	9.43e-01	1.0000000	ns	p = 1	0.0067643	small
Random	Logic-9	100	value	Phenotypic	Phylogenetic	60	60	1753.5	7.85e-01	1.0000000	ns	p = 1	0.0251621	small
Random	Logic-9	1000	value	Phenotypic	Phylogenetic	60	60	1730.0	6.23e-01	1.0000000	ns	p = 1	0.0452501	small
Random	NK Landscape	10	value	Phenotypic	Phylogenetic	60	60	1158.0	7.60e-04	0.0448400		p = 0.04484	0.3076034	moderate
Random	NK Landscape	100	value	Phenotypic	Phylogenetic	60	60	1087.0	1.84e-04	0.0108560		p = 0.010856	0.3416218	moderate
Random	NK Landscape	1000	value	Phenotypic	Phylogenetic	60	60	822.0	3.00e-07	0.0000171	****	p < 1e-04	0.4685921	moderate
Random	Sorting network	10	value	Phenotypic	Phylogenetic	60	60	1849.0	7.99e-01	1.0000000	ns	p = 1	0.0234775	small
Random	Sorting network	100	value	Phenotypic	Phylogenetic	60	60	1072.0	1.34e-04	0.0079060	**	p = 0.007906	0.3488088	moderate
Random	Sorting network	1000	value	Phenotypic	Phylogenetic	60	60	895.0	2.10e-06	0.0001215	***	p = 0.00012154	0.4336153	moderate
Tournament	Count Odds	10	value	Phenotypic	Phylogenetic	60	60	1545.0	1.82e-01	1.0000000	ns	p = 1	0.1221789	small
Tournament	Count Odds	100	value	Phenotypic	Phylogenetic	60	60	1196.0	1.54e-03	0.0908600	ns	p = 0.09086	0.2893963	small
Tournament	Count Odds	1000	value	Phenotypic	Phylogenetic	60	60	1821.5	9.12e-01	1.0000000	ns	p = 1	0.0103029	small
Tournament	Logic-9	10	value	Phenotypic	Phylogenetic	60	60	1895.0	6.20e-01	1.0000000	ns	p = 1	0.0455184	small
Tournament	Logic-9	100	value	Phenotypic	Phylogenetic	60	60	1727.0	7.04e-01	1.0000000	ns	p = 1	0.0349773	small
Tournament	Logic-9	1000	value	Phenotypic	Phylogenetic	60	60	1715.0	6.54e-01	1.0000000	ns	p = 1	0.0411561	small
Tournament	NK Landscape	10	value	Phenotypic	Phylogenetic	60	60	1794.0	9.61e-01	1.0000000	ns	p = 1	0.0048659	small
Tournament	NK Landscape	100	value	Phenotypic	Phylogenetic	60	60	1782.0	8.76e-01	1.0000000	ns	p = 1	0.0145977	small
Tournament	NK Landscape	1000	value	Phenotypic	Phylogenetic	60	60	1784.0	8.90e-01	1.0000000	ns	p = 1	0.0129757	small
Tournament	Sorting network	10	value	Phenotypic	Phylogenetic	60	60	1760.5	8.38e-01	1.0000000	ns	p = 1	0.0189269	small
Tournament	Sorting network	100	value	Phenotypic	Phylogenetic	60	60	1335.0	1.48e-02	0.8732000	ns	p = 0.8732	0.2227968	small
Tournament	Sorting network	1000	value	Phenotypic	Phylogenetic	60	60	1833.5	8.54e-01	1.0000000	ns	p = 1	0.0170991	small

Mean pairwise distance vs. phenotypic Shannon diversity

res <- data %>% group_by(SEED, selection_name, problem_name) %>%
summarise(
  fit_phylo_10 = condinformation(discretize(max_performance), discretize(lag(mean_phenotype_pairwise_distance, 1)), discretize(lag(max_performance, 1))),
  fit_phylo_100 = condinformation(discretize(max_performance), discretize(lag(mean_phenotype_pairwise_distance, 10)), discretize(lag(max_performance, 10))),
  fit_phylo_1000 = condinformation(discretize(max_performance), discretize(lag(mean_phenotype_pairwise_distance, 100)), discretize(lag(max_performance, 100))),
    fit_pheno_10 = condinformation(discretize(max_performance), discretize(lag(phenotype_diversity, 1)), discretize(lag(max_performance, 1))),
      fit_pheno_100 = condinformation(discretize(max_performance), discretize(lag(phenotype_diversity, 10)), discretize(lag(max_performance, 10))),
      fit_pheno_1000 = condinformation(discretize(max_performance), discretize(lag(phenotype_diversity, 100)), discretize(lag(max_performance, 100)))
      )

res <- res %>% pivot_longer(cols=contains("o_10"))
res$offset <- str_extract(res$name, "[:digit:]*$")
res$Type <- case_when(str_detect(res$name, "phylo") ~ "Phylogenetic", TRUE ~ "Phenotypic")

ggplot(
  res %>% filter(str_detect(name, "fit_ph*")), 
  aes(
    x=as.factor(offset), 
    y=value, 
    color=Type
    )
  ) + 
  geom_boxplot() + 
  facet_wrap(~selection_name*problem_name, ncol=4) + 
  scale_x_discrete("Lag") + 
  scale_y_continuous("Transfer Entropy") + 
  scale_color_discrete("") + 
  theme(legend.position = "bottom")

# Determine which conditions are significantly different from each other
transfer_entropy_stats(res)

selection_name	problem_name	offset	.y.	group1	group2	n1	n2	statistic	p	p.adj	p.adj.signif	label	effsize	magnitude
Eco-EA	Count Odds	10	value	Phenotypic	Phylogenetic	60	60	1749.0	7.91e-01	1.0000000	ns	p = 1	0.0244358	small
Eco-EA	Count Odds	100	value	Phenotypic	Phylogenetic	60	60	1190.0	1.38e-03	0.0814200	ns	p = 0.08142	0.2922711	small
Eco-EA	Count Odds	1000	value	Phenotypic	Phylogenetic	60	60	1328.0	1.33e-02	0.7847000	ns	p = 0.7847	0.2261547	small
Eco-EA	Logic-9	10	value	Phenotypic	Phylogenetic	60	60	1746.0	7.79e-01	1.0000000	ns	p = 1	0.0258736	small
Eco-EA	Logic-9	100	value	Phenotypic	Phylogenetic	60	60	1703.0	6.13e-01	1.0000000	ns	p = 1	0.0464767	small
Eco-EA	Logic-9	1000	value	Phenotypic	Phylogenetic	60	60	1517.0	1.36e-01	1.0000000	ns	p = 1	0.1362109	small
Eco-EA	NK Landscape	10	value	Phenotypic	Phylogenetic	60	60	1721.5	6.82e-01	1.0000000	ns	p = 1	0.0376120	small
Eco-EA	NK Landscape	100	value	Phenotypic	Phylogenetic	60	60	1595.5	2.84e-01	1.0000000	ns	p = 1	0.0979829	small
Eco-EA	NK Landscape	1000	value	Phenotypic	Phylogenetic	60	60	1744.0	7.71e-01	1.0000000	ns	p = 1	0.0268319	small
Eco-EA	Sorting network	10	value	Phenotypic	Phylogenetic	60	60	1804.0	9.85e-01	1.0000000	ns	p = 1	0.0019190	small
Eco-EA	Sorting network	100	value	Phenotypic	Phylogenetic	60	60	1145.0	5.91e-04	0.0348690		p = 0.034869	0.3138561	moderate
Eco-EA	Sorting network	1000	value	Phenotypic	Phylogenetic	60	60	1799.0	9.93e-01	1.0000000	ns	p = 1	0.0015407	small
Fitness sharing	Count Odds	10	value	Phenotypic	Phylogenetic	60	60	1670.0	4.97e-01	1.0000000	ns	p = 1	0.0622873	small
Fitness sharing	Count Odds	100	value	Phenotypic	Phylogenetic	60	60	1207.0	1.87e-03	0.1103300	ns	p = 0.11033	0.2841259	small
Fitness sharing	Count Odds	1000	value	Phenotypic	Phylogenetic	60	60	1555.0	1.99e-01	1.0000000	ns	p = 1	0.1173876	small
Fitness sharing	Logic-9	10	value	Phenotypic	Phylogenetic	60	60	1573.0	2.35e-01	1.0000000	ns	p = 1	0.1087651	small
Fitness sharing	Logic-9	100	value	Phenotypic	Phylogenetic	60	60	1313.0	1.07e-02	0.6313000	ns	p = 0.6313	0.2333418	small
Fitness sharing	Logic-9	1000	value	Phenotypic	Phylogenetic	60	60	1455.0	6.98e-02	1.0000000	ns	p = 1	0.1657446	small
Fitness sharing	NK Landscape	10	value	Phenotypic	Phylogenetic	60	60	1268.0	5.28e-03	0.3115200	ns	p = 0.31152	0.2548987	small
Fitness sharing	NK Landscape	100	value	Phenotypic	Phylogenetic	60	60	691.0	0.00e+00	0.0000004	****	p < 1e-04	0.5313585	large
Fitness sharing	NK Landscape	1000	value	Phenotypic	Phylogenetic	60	60	617.0	0.00e+00	0.0000000	****	p < 1e-04	0.5668143	large
Fitness sharing	Sorting network	10	value	Phenotypic	Phylogenetic	60	60	874.0	1.20e-06	0.0000702	****	p < 1e-04	0.4436771	moderate
Fitness sharing	Sorting network	100	value	Phenotypic	Phylogenetic	60	60	332.0	0.00e+00	0.0000000	****	p < 1e-04	0.7033672	large
Fitness sharing	Sorting network	1000	value	Phenotypic	Phylogenetic	60	60	906.0	2.70e-06	0.0001617	***	p = 0.00016166	0.4283449	moderate
Lexicase	Count Odds	10	value	Phenotypic	Phylogenetic	60	60	1404.0	3.79e-02	1.0000000	ns	p = 1	0.1897367	small
Lexicase	Count Odds	100	value	Phenotypic	Phylogenetic	60	60	368.0	0.00e+00	0.0000000	****	p < 1e-04	0.6861184	large
Lexicase	Count Odds	1000	value	Phenotypic	Phylogenetic	60	60	827.0	3.00e-07	0.0000196	****	p < 1e-04	0.4661964	moderate
Lexicase	Logic-9	10	value	Phenotypic	Phylogenetic	60	60	1722.5	6.86e-01	1.0000000	ns	p = 1	0.0371329	small
Lexicase	Logic-9	100	value	Phenotypic	Phylogenetic	60	60	1579.5	2.48e-01	1.0000000	ns	p = 1	0.1056490	small
Lexicase	Logic-9	1000	value	Phenotypic	Phylogenetic	60	60	1617.0	3.36e-01	1.0000000	ns	p = 1	0.0880337	small
Lexicase	NK Landscape	10	value	Phenotypic	Phylogenetic	60	60	1755.0	8.14e-01	1.0000000	ns	p = 1	0.0216991	small
Lexicase	NK Landscape	100	value	Phenotypic	Phylogenetic	60	60	1327.0	1.26e-02	0.7434000	ns	p = 0.7434	0.2280815	small
Lexicase	NK Landscape	1000	value	Phenotypic	Phylogenetic	60	60	971.0	1.21e-05	0.0007139	***	p = 0.0007139	0.3997454	moderate
Lexicase	Sorting network	10	value	Phenotypic	Phylogenetic	60	60	1785.5	9.25e-01	1.0000000	ns	p = 1	0.0089276	small
Lexicase	Sorting network	100	value	Phenotypic	Phylogenetic	60	60	1748.0	7.28e-01	1.0000000	ns	p = 1	0.0320154	small
Random	Count Odds	10	value	Phenotypic	Phylogenetic	60	60	1776.0	9.02e-01	1.0000000	ns	p = 1	0.0114992	small
Random	Count Odds	100	value	Phenotypic	Phylogenetic	60	60	1991.0	3.17e-01	1.0000000	ns	p = 1	0.0915144	small
Random	Count Odds	1000	value	Phenotypic	Phylogenetic	60	60	1110.0	2.96e-04	0.0174640		p = 0.017464	0.3306018	moderate
Random	Logic-9	10	value	Phenotypic	Phylogenetic	60	60	1934.0	4.28e-01	1.0000000	ns	p = 1	0.0725501	small
Random	Logic-9	100	value	Phenotypic	Phylogenetic	60	60	1854.5	7.49e-01	1.0000000	ns	p = 1	0.0294925	small
Random	Logic-9	1000	value	Phenotypic	Phylogenetic	60	60	1749.0	7.21e-01	1.0000000	ns	p = 1	0.0329683	small
Random	NK Landscape	10	value	Phenotypic	Phylogenetic	60	60	1063.0	1.11e-04	0.0065490	**	p = 0.006549	0.3531210	moderate
Random	NK Landscape	100	value	Phenotypic	Phylogenetic	60	60	1322.0	1.22e-02	0.7198000	ns	p = 0.7198	0.2290256	small
Random	NK Landscape	1000	value	Phenotypic	Phylogenetic	60	60	865.0	9.00e-07	0.0000552	****	p < 1e-04	0.4479893	moderate
Random	Sorting network	10	value	Phenotypic	Phylogenetic	60	60	1731.0	7.19e-01	1.0000000	ns	p = 1	0.0330602	small
Random	Sorting network	100	value	Phenotypic	Phylogenetic	60	60	1397.0	3.46e-02	1.0000000	ns	p = 1	0.1930906	small
Random	Sorting network	1000	value	Phenotypic	Phylogenetic	60	60	1008.0	3.26e-05	0.0019234	**	p = 0.0019234	0.3794733	moderate
Tournament	Count Odds	10	value	Phenotypic	Phylogenetic	60	60	1601.0	2.97e-01	1.0000000	ns	p = 1	0.0953475	small
Tournament	Count Odds	100	value	Phenotypic	Phylogenetic	60	60	1368.0	2.35e-02	1.0000000	ns	p = 1	0.2069854	small
Tournament	Count Odds	1000	value	Phenotypic	Phylogenetic	60	60	1761.0	8.40e-01	1.0000000	ns	p = 1	0.0186901	small
Tournament	Logic-9	10	value	Phenotypic	Phylogenetic	60	60	1790.5	9.62e-01	1.0000000	ns	p = 1	0.0045519	small
Tournament	Logic-9	100	value	Phenotypic	Phylogenetic	60	60	1731.0	7.19e-01	1.0000000	ns	p = 1	0.0330607	small
Tournament	Logic-9	1000	value	Phenotypic	Phylogenetic	60	60	1601.0	2.93e-01	1.0000000	ns	p = 1	0.0962637	small
Tournament	NK Landscape	10	value	Phenotypic	Phylogenetic	60	60	1794.5	9.65e-01	1.0000000	ns	p = 1	0.0044604	small
Tournament	NK Landscape	100	value	Phenotypic	Phylogenetic	60	60	1794.0	9.61e-01	1.0000000	ns	p = 1	0.0048659	small
Tournament	NK Landscape	1000	value	Phenotypic	Phylogenetic	60	60	1800.0	1.00e+00	1.0000000	ns	p = 1	0.0000000	small
Tournament	Sorting network	10	value	Phenotypic	Phylogenetic	60	60	1811.5	9.54e-01	1.0000000	ns	p = 1	0.0055104	small
Tournament	Sorting network	100	value	Phenotypic	Phylogenetic	60	60	1548.5	1.88e-01	1.0000000	ns	p = 1	0.1205024	small
Tournament	Sorting network	1000	value	Phenotypic	Phylogenetic	60	60	1779.0	9.09e-01	1.0000000	ns	p = 1	0.0107189	small

Mean evolutionary distinctiveness vs. phenotypic richness

res <- data %>% group_by(SEED, selection_name, problem_name) %>%
summarise(
  fit_phylo_10 = condinformation(discretize(max_performance), discretize(lag(mean_phenotype_evolutionary_distinctiveness, 1)), discretize(lag(max_performance, 1))),
  fit_phylo_100 = condinformation(discretize(max_performance), discretize(lag(mean_phenotype_evolutionary_distinctiveness, 10)), discretize(lag(max_performance, 10))),
  fit_phylo_1000 = condinformation(discretize(max_performance), discretize(lag(mean_phenotype_evolutionary_distinctiveness, 100)), discretize(lag(max_performance, 100))),
    fit_pheno_10 = condinformation(discretize(max_performance), discretize(lag(phenotype_num_taxa, 1)), discretize(lag(max_performance, 1))),
      fit_pheno_100 = condinformation(discretize(max_performance), discretize(lag(phenotype_num_taxa, 10)), discretize(lag(max_performance, 10))),
      fit_pheno_1000 = condinformation(discretize(max_performance), discretize(lag(phenotype_num_taxa, 100)), discretize(lag(max_performance, 100)))
      )

res <- res %>% pivot_longer(cols=contains("o_10"))
res$offset <- str_extract(res$name, "[:digit:]*$")
res$Type <- case_when(str_detect(res$name, "phylo") ~ "Phylogenetic", TRUE ~ "Phenotypic")

ggplot(
  res %>% filter(str_detect(name, "fit_ph*")), 
  aes(
    x=as.factor(offset), 
    y=value, 
    color=Type
    )
  ) + 
  geom_boxplot() + 
  facet_wrap(~selection_name*problem_name, ncol=4) + 
  scale_x_discrete("Lag") + 
  scale_y_continuous("Transfer Entropy") + 
  scale_color_discrete("") + 
  theme(legend.position = "bottom")

# Determine which conditions are significantly different from each other
transfer_entropy_stats(res)

selection_name	problem_name	offset	.y.	group1	group2	n1	n2	statistic	p	p.adj	p.adj.signif	label	effsize	magnitude
Eco-EA	Count Odds	10	value	Phenotypic	Phylogenetic	60	60	1653.0	4.42e-01	1.0000000	ns	p = 1	0.0704325	small
Eco-EA	Count Odds	100	value	Phenotypic	Phylogenetic	60	60	1180.0	1.15e-03	0.0678500	ns	p = 0.06785	0.2970624	small
Eco-EA	Count Odds	1000	value	Phenotypic	Phylogenetic	60	60	1315.0	1.10e-02	0.6490000	ns	p = 0.649	0.2323835	small
Eco-EA	Logic-9	10	value	Phenotypic	Phylogenetic	60	60	1842.0	8.28e-01	1.0000000	ns	p = 1	0.0201239	small
Eco-EA	Logic-9	100	value	Phenotypic	Phylogenetic	60	60	1556.0	2.01e-01	1.0000000	ns	p = 1	0.1169105	small
Eco-EA	Logic-9	1000	value	Phenotypic	Phylogenetic	60	60	1591.0	2.72e-01	1.0000000	ns	p = 1	0.1005939	small
Eco-EA	NK Landscape	10	value	Phenotypic	Phylogenetic	60	60	1417.5	4.50e-02	1.0000000	ns	p = 1	0.1832687	small
Eco-EA	NK Landscape	100	value	Phenotypic	Phylogenetic	60	60	1487.5	1.02e-01	1.0000000	ns	p = 1	0.1497293	small
Eco-EA	NK Landscape	1000	value	Phenotypic	Phylogenetic	60	60	1505.0	1.22e-01	1.0000000	ns	p = 1	0.1413467	small
Eco-EA	Sorting network	10	value	Phenotypic	Phylogenetic	60	60	1674.0	5.10e-01	1.0000000	ns	p = 1	0.0604466	small
Eco-EA	Sorting network	100	value	Phenotypic	Phylogenetic	60	60	1269.5	5.40e-03	0.3186000	ns	p = 0.3186	0.2541924	small
Eco-EA	Sorting network	1000	value	Phenotypic	Phylogenetic	60	60	1798.0	9.80e-01	1.0000000	ns	p = 1	0.0030814	small
Fitness sharing	Count Odds	10	value	Phenotypic	Phylogenetic	60	60	1721.0	6.80e-01	1.0000000	ns	p = 1	0.0378515	small
Fitness sharing	Count Odds	100	value	Phenotypic	Phylogenetic	60	60	1518.0	1.40e-01	1.0000000	ns	p = 1	0.1351155	small
Fitness sharing	Count Odds	1000	value	Phenotypic	Phylogenetic	60	60	1870.0	7.15e-01	1.0000000	ns	p = 1	0.0335393	small
Fitness sharing	Logic-9	10	value	Phenotypic	Phylogenetic	60	60	1611.0	3.22e-01	1.0000000	ns	p = 1	0.0905577	small
Fitness sharing	Logic-9	100	value	Phenotypic	Phylogenetic	60	60	1667.0	4.87e-01	1.0000000	ns	p = 1	0.0637258	small
Fitness sharing	Logic-9	1000	value	Phenotypic	Phylogenetic	60	60	1535.0	1.64e-01	1.0000000	ns	p = 1	0.1273111	small
Fitness sharing	NK Landscape	10	value	Phenotypic	Phylogenetic	60	60	1238.0	3.21e-03	0.1893900	ns	p = 0.18939	0.2692727	small
Fitness sharing	NK Landscape	100	value	Phenotypic	Phylogenetic	60	60	894.0	2.00e-06	0.0001186	***	p = 0.00011859	0.4340945	moderate
Fitness sharing	NK Landscape	1000	value	Phenotypic	Phylogenetic	60	60	956.0	9.60e-06	0.0005634	***	p = 0.00056345	0.4043882	moderate
Fitness sharing	Sorting network	10	value	Phenotypic	Phylogenetic	60	60	972.0	1.40e-05	0.0008260	***	p = 0.000826	0.3967221	moderate
Fitness sharing	Sorting network	100	value	Phenotypic	Phylogenetic	60	60	1065.0	1.16e-04	0.0068440	**	p = 0.006844	0.3521627	moderate
Fitness sharing	Sorting network	1000	value	Phenotypic	Phylogenetic	60	60	1780.0	9.18e-01	1.0000000	ns	p = 1	0.0095827	small
Lexicase	Count Odds	10	value	Phenotypic	Phylogenetic	60	60	1977.0	3.54e-01	1.0000000	ns	p = 1	0.0848065	small
Lexicase	Count Odds	100	value	Phenotypic	Phylogenetic	60	60	791.0	1.00e-07	0.0000071	****	p < 1e-04	0.4834452	moderate
Lexicase	Count Odds	1000	value	Phenotypic	Phylogenetic	60	60	1038.0	6.42e-05	0.0037878	**	p = 0.0037878	0.3650993	moderate
Lexicase	Logic-9	10	value	Phenotypic	Phylogenetic	60	60	1873.5	7.02e-01	1.0000000	ns	p = 1	0.0352163	small
Lexicase	Logic-9	100	value	Phenotypic	Phylogenetic	60	60	1266.5	5.15e-03	0.3038500	ns	p = 0.30385	0.2556179	small
Lexicase	Logic-9	1000	value	Phenotypic	Phylogenetic	60	60	1660.5	4.64e-01	1.0000000	ns	p = 1	0.0671430	small
Lexicase	NK Landscape	10	value	Phenotypic	Phylogenetic	60	60	1755.0	8.14e-01	1.0000000	ns	p = 1	0.0216991	small
Lexicase	NK Landscape	100	value	Phenotypic	Phylogenetic	60	60	1455.0	6.88e-02	1.0000000	ns	p = 1	0.1663597	small
Lexicase	NK Landscape	1000	value	Phenotypic	Phylogenetic	60	60	1121.0	3.38e-04	0.0199420		p = 0.019942	0.3274151	moderate
Lexicase	Sorting network	10	value	Phenotypic	Phylogenetic	60	60	1794.5	9.73e-01	1.0000000	ns	p = 1	0.0033862	small
Lexicase	Sorting network	100	value	Phenotypic	Phylogenetic	60	60	1735.0	6.64e-01	1.0000000	ns	p = 1	0.0400189	small
Random	Count Odds	10	value	Phenotypic	Phylogenetic	60	60	1583.0	2.56e-01	1.0000000	ns	p = 1	0.1039719	small
Random	Count Odds	100	value	Phenotypic	Phylogenetic	60	60	1932.0	4.90e-01	1.0000000	ns	p = 1	0.0632456	small
Random	Count Odds	1000	value	Phenotypic	Phylogenetic	60	60	1462.0	7.65e-02	1.0000000	ns	p = 1	0.1619469	small
Random	Logic-9	10	value	Phenotypic	Phylogenetic	60	60	1705.0	5.75e-01	1.0000000	ns	p = 1	0.0514143	small
Random	Logic-9	100	value	Phenotypic	Phylogenetic	60	60	1733.0	6.93e-01	1.0000000	ns	p = 1	0.0362562	small
Random	Logic-9	1000	value	Phenotypic	Phylogenetic	60	60	1771.5	8.43e-01	1.0000000	ns	p = 1	0.0184230	small
Random	NK Landscape	10	value	Phenotypic	Phylogenetic	60	60	1288.0	7.26e-03	0.4283400	ns	p = 0.42834	0.2453161	small
Random	NK Landscape	100	value	Phenotypic	Phylogenetic	60	60	1196.0	1.54e-03	0.0908600	ns	p = 0.09086	0.2893963	small
Random	NK Landscape	1000	value	Phenotypic	Phylogenetic	60	60	1028.0	5.14e-05	0.0030326	**	p = 0.0030326	0.3698907	moderate
Random	Sorting network	10	value	Phenotypic	Phylogenetic	60	60	2172.0	5.12e-02	1.0000000	ns	p = 1	0.1782375	small
Random	Sorting network	100	value	Phenotypic	Phylogenetic	60	60	1603.0	3.02e-01	1.0000000	ns	p = 1	0.0943892	small
Random	Sorting network	1000	value	Phenotypic	Phylogenetic	60	60	1629.0	3.71e-01	1.0000000	ns	p = 1	0.0819317	small
Tournament	Count Odds	10	value	Phenotypic	Phylogenetic	60	60	1570.0	2.28e-01	1.0000000	ns	p = 1	0.1102006	small
Tournament	Count Odds	100	value	Phenotypic	Phylogenetic	60	60	1026.0	4.91e-05	0.0028969	**	p = 0.0028969	0.3708489	moderate
Tournament	Count Odds	1000	value	Phenotypic	Phylogenetic	60	60	1522.5	1.46e-01	1.0000000	ns	p = 1	0.1329675	small
Tournament	Logic-9	10	value	Phenotypic	Phylogenetic	60	60	1991.0	3.17e-01	1.0000000	ns	p = 1	0.0915160	small
Tournament	Logic-9	100	value	Phenotypic	Phylogenetic	60	60	1309.0	1.00e-02	0.5900000	ns	p = 0.59	0.2352588	small
Tournament	Logic-9	1000	value	Phenotypic	Phylogenetic	60	60	1604.0	3.00e-01	1.0000000	ns	p = 1	0.0949012	small
Tournament	NK Landscape	10	value	Phenotypic	Phylogenetic	60	60	1819.0	8.69e-01	1.0000000	ns	p = 1	0.0154086	small
Tournament	NK Landscape	100	value	Phenotypic	Phylogenetic	60	60	1780.0	8.62e-01	1.0000000	ns	p = 1	0.0162196	small
Tournament	NK Landscape	1000	value	Phenotypic	Phylogenetic	60	60	1774.0	8.21e-01	1.0000000	ns	p = 1	0.0210855	small
Tournament	Sorting network	10	value	Phenotypic	Phylogenetic	60	60	1784.5	9.37e-01	1.0000000	ns	p = 1	0.0074270	small
Tournament	Sorting network	100	value	Phenotypic	Phylogenetic	60	60	854.0	7.00e-07	0.0000411	****	p < 1e-04	0.4532606	moderate
Tournament	Sorting network	1000	value	Phenotypic	Phylogenetic	60	60	1750.5	7.84e-01	1.0000000	ns	p = 1	0.0252657	small

Mean evolutionary distinctiveness vs. phenotypic Shannon diveristy

res <- data %>% group_by(SEED, selection_name, problem_name) %>%
summarise(
  fit_phylo_10 = condinformation(discretize(max_performance), discretize(lag(mean_phenotype_evolutionary_distinctiveness, 1)), discretize(lag(max_performance, 1))),
  fit_phylo_100 = condinformation(discretize(max_performance), discretize(lag(mean_phenotype_evolutionary_distinctiveness, 10)), discretize(lag(max_performance, 10))),
  fit_phylo_1000 = condinformation(discretize(max_performance), discretize(lag(mean_phenotype_evolutionary_distinctiveness, 100)), discretize(lag(max_performance, 100))),
    fit_pheno_10 = condinformation(discretize(max_performance), discretize(lag(phenotype_diversity, 1)), discretize(lag(max_performance, 1))),
      fit_pheno_100 = condinformation(discretize(max_performance), discretize(lag(phenotype_diversity, 10)), discretize(lag(max_performance, 10))),
      fit_pheno_1000 = condinformation(discretize(max_performance), discretize(lag(phenotype_diversity, 100)), discretize(lag(max_performance, 100)))
      )

res <- res %>% pivot_longer(cols=contains("o_10"))
res$offset <- str_extract(res$name, "[:digit:]*$")
res$Type <- case_when(str_detect(res$name, "phylo") ~ "Phylogenetic", TRUE ~ "Phenotypic")

ggplot(
  res %>% filter(str_detect(name, "fit_ph*")), 
  aes(
    x=as.factor(offset), 
    y=value, 
    color=Type
    )
  ) + 
  geom_boxplot() + 
  facet_wrap(~selection_name*problem_name, ncol=4) + 
  scale_x_discrete("Lag") + 
  scale_y_continuous("Transfer Entropy") + 
  scale_color_discrete("") + 
  theme(legend.position = "bottom")

# Determine which conditions are significantly different from each other
transfer_entropy_stats(res)

selection_name	problem_name	offset	.y.	group1	group2	n1	n2	statistic	p	p.adj	p.adj.signif	label	effsize	magnitude
Eco-EA	Count Odds	10	value	Phenotypic	Phylogenetic	60	60	1740.0	7.55e-01	1.0000000	ns	p = 1	0.0287480	small
Eco-EA	Count Odds	100	value	Phenotypic	Phylogenetic	60	60	1389.0	3.12e-02	1.0000000	ns	p = 1	0.1969237	small
Eco-EA	Count Odds	1000	value	Phenotypic	Phylogenetic	60	60	1325.0	1.28e-02	0.7552000	ns	p = 0.7552	0.2275921	small
Eco-EA	Logic-9	10	value	Phenotypic	Phylogenetic	60	60	1826.0	8.94e-01	1.0000000	ns	p = 1	0.0124577	small
Eco-EA	Logic-9	100	value	Phenotypic	Phylogenetic	60	60	1565.0	2.18e-01	1.0000000	ns	p = 1	0.1125982	small
Eco-EA	Logic-9	1000	value	Phenotypic	Phylogenetic	60	60	1441.5	5.89e-02	1.0000000	ns	p = 1	0.1726482	small
Eco-EA	NK Landscape	10	value	Phenotypic	Phylogenetic	60	60	1631.5	3.78e-01	1.0000000	ns	p = 1	0.0807340	small
Eco-EA	NK Landscape	100	value	Phenotypic	Phylogenetic	60	60	1524.5	1.49e-01	1.0000000	ns	p = 1	0.1320014	small
Eco-EA	NK Landscape	1000	value	Phenotypic	Phylogenetic	60	60	1469.0	8.28e-02	1.0000000	ns	p = 1	0.1585958	small
Eco-EA	Sorting network	10	value	Phenotypic	Phylogenetic	60	60	1667.5	4.88e-01	1.0000000	ns	p = 1	0.0635682	small
Eco-EA	Sorting network	100	value	Phenotypic	Phylogenetic	60	60	789.0	1.00e-07	0.0000067	****	p < 1e-04	0.4844421	moderate
Eco-EA	Sorting network	1000	value	Phenotypic	Phylogenetic	60	60	1798.0	9.80e-01	1.0000000	ns	p = 1	0.0030814	small
Fitness sharing	Count Odds	10	value	Phenotypic	Phylogenetic	60	60	1733.0	7.27e-01	1.0000000	ns	p = 1	0.0321019	small
Fitness sharing	Count Odds	100	value	Phenotypic	Phylogenetic	60	60	1431.0	5.31e-02	1.0000000	ns	p = 1	0.1768001	small
Fitness sharing	Count Odds	1000	value	Phenotypic	Phylogenetic	60	60	1823.0	9.06e-01	1.0000000	ns	p = 1	0.0110201	small
Fitness sharing	Logic-9	10	value	Phenotypic	Phylogenetic	60	60	1722.0	6.84e-01	1.0000000	ns	p = 1	0.0373730	small
Fitness sharing	Logic-9	100	value	Phenotypic	Phylogenetic	60	60	1727.0	7.04e-01	1.0000000	ns	p = 1	0.0349773	small
Fitness sharing	Logic-9	1000	value	Phenotypic	Phylogenetic	60	60	1455.0	6.98e-02	1.0000000	ns	p = 1	0.1657446	small
Fitness sharing	NK Landscape	10	value	Phenotypic	Phylogenetic	60	60	1218.0	2.27e-03	0.1339300	ns	p = 0.13393	0.2788554	small
Fitness sharing	NK Landscape	100	value	Phenotypic	Phylogenetic	60	60	911.0	3.10e-06	0.0001835	***	p = 0.00018349	0.4259492	moderate
Fitness sharing	NK Landscape	1000	value	Phenotypic	Phylogenetic	60	60	877.0	1.30e-06	0.0000761	****	p < 1e-04	0.4422397	moderate
Fitness sharing	Sorting network	10	value	Phenotypic	Phylogenetic	60	60	907.0	2.80e-06	0.0001658	***	p = 0.00016579	0.4278658	moderate
Fitness sharing	Sorting network	100	value	Phenotypic	Phylogenetic	60	60	941.0	6.60e-06	0.0003900	***	p = 0.00038999	0.4115752	moderate
Fitness sharing	Sorting network	1000	value	Phenotypic	Phylogenetic	60	60	1587.0	2.65e-01	1.0000000	ns	p = 1	0.1020560	small
Lexicase	Count Odds	10	value	Phenotypic	Phylogenetic	60	60	1891.0	6.35e-01	1.0000000	ns	p = 1	0.0436011	small
Lexicase	Count Odds	100	value	Phenotypic	Phylogenetic	60	60	716.0	0.00e+00	0.0000008	****	p < 1e-04	0.5193801	large
Lexicase	Count Odds	1000	value	Phenotypic	Phylogenetic	60	60	1038.0	6.42e-05	0.0037878	**	p = 0.0037878	0.3650993	moderate
Lexicase	Logic-9	10	value	Phenotypic	Phylogenetic	60	60	1837.5	8.46e-01	1.0000000	ns	p = 1	0.0179675	small
Lexicase	Logic-9	100	value	Phenotypic	Phylogenetic	60	60	1370.5	2.43e-02	1.0000000	ns	p = 1	0.2057880	small
Lexicase	Logic-9	1000	value	Phenotypic	Phylogenetic	60	60	1668.0	4.88e-01	1.0000000	ns	p = 1	0.0636086	small
Lexicase	NK Landscape	10	value	Phenotypic	Phylogenetic	60	60	1774.0	8.93e-01	1.0000000	ns	p = 1	0.0125373	small
Lexicase	NK Landscape	100	value	Phenotypic	Phylogenetic	60	60	1418.0	4.39e-02	1.0000000	ns	p = 1	0.1842011	small
Lexicase	NK Landscape	1000	value	Phenotypic	Phylogenetic	60	60	1044.0	6.59e-05	0.0038881	**	p = 0.0038881	0.3645447	moderate
Lexicase	Sorting network	10	value	Phenotypic	Phylogenetic	60	60	1742.0	6.98e-01	1.0000000	ns	p = 1	0.0357093	small
Lexicase	Sorting network	100	value	Phenotypic	Phylogenetic	60	60	1722.0	6.01e-01	1.0000000	ns	p = 1	0.0480229	small
Random	Count Odds	10	value	Phenotypic	Phylogenetic	60	60	1610.0	3.20e-01	1.0000000	ns	p = 1	0.0910353	small
Random	Count Odds	100	value	Phenotypic	Phylogenetic	60	60	1961.0	4.00e-01	1.0000000	ns	p = 1	0.0771404	small
Random	Count Odds	1000	value	Phenotypic	Phylogenetic	60	60	1478.0	9.15e-02	1.0000000	ns	p = 1	0.1542808	small
Random	Logic-9	10	value	Phenotypic	Phylogenetic	60	60	1826.0	8.80e-01	1.0000000	ns	p = 1	0.0140841	small
Random	Logic-9	100	value	Phenotypic	Phylogenetic	60	60	1773.5	8.77e-01	1.0000000	ns	p = 1	0.0143423	small
Random	Logic-9	1000	value	Phenotypic	Phylogenetic	60	60	1813.0	9.29e-01	1.0000000	ns	p = 1	0.0084038	small
Random	NK Landscape	10	value	Phenotypic	Phylogenetic	60	60	1240.0	3.32e-03	0.1958800	ns	p = 0.19588	0.2683145	small
Random	NK Landscape	100	value	Phenotypic	Phylogenetic	60	60	1437.0	5.71e-02	1.0000000	ns	p = 1	0.1739253	small
Random	NK Landscape	1000	value	Phenotypic	Phylogenetic	60	60	1089.0	1.92e-04	0.0113280		p = 0.011328	0.3406635	moderate
Random	Sorting network	10	value	Phenotypic	Phylogenetic	60	60	2056.0	1.80e-01	1.0000000	ns	p = 1	0.1226580	small
Random	Sorting network	100	value	Phenotypic	Phylogenetic	60	60	1935.0	4.80e-01	1.0000000	ns	p = 1	0.0646830	small
Random	Sorting network	1000	value	Phenotypic	Phylogenetic	60	60	1739.0	7.51e-01	1.0000000	ns	p = 1	0.0292271	small
Tournament	Count Odds	10	value	Phenotypic	Phylogenetic	60	60	1606.0	3.10e-01	1.0000000	ns	p = 1	0.0929518	small
Tournament	Count Odds	100	value	Phenotypic	Phylogenetic	60	60	1217.0	2.23e-03	0.1315700	ns	p = 0.13157	0.2793345	small
Tournament	Count Odds	1000	value	Phenotypic	Phylogenetic	60	60	1487.0	1.01e-01	1.0000000	ns	p = 1	0.1499832	small
Tournament	Logic-9	10	value	Phenotypic	Phylogenetic	60	60	1879.0	6.80e-01	1.0000000	ns	p = 1	0.0378523	small
Tournament	Logic-9	100	value	Phenotypic	Phylogenetic	60	60	1337.0	1.52e-02	0.8968000	ns	p = 0.8968	0.2218428	small
Tournament	Logic-9	1000	value	Phenotypic	Phylogenetic	60	60	1517.0	1.34e-01	1.0000000	ns	p = 1	0.1368976	small
Tournament	NK Landscape	10	value	Phenotypic	Phylogenetic	60	60	1816.0	8.90e-01	1.0000000	ns	p = 1	0.0129757	small
Tournament	NK Landscape	100	value	Phenotypic	Phylogenetic	60	60	1785.0	8.98e-01	1.0000000	ns	p = 1	0.0121647	small
Tournament	NK Landscape	1000	value	Phenotypic	Phylogenetic	60	60	1782.0	8.76e-01	1.0000000	ns	p = 1	0.0145977	small
Tournament	Sorting network	10	value	Phenotypic	Phylogenetic	60	60	1859.5	7.57e-01	1.0000000	ns	p = 1	0.0285101	small
Tournament	Sorting network	100	value	Phenotypic	Phylogenetic	60	60	1063.0	1.11e-04	0.0065490	**	p = 0.006549	0.3531222	moderate
Tournament	Sorting network	1000	value	Phenotypic	Phylogenetic	60	60	1717.5	6.47e-01	1.0000000	ns	p = 1	0.0421095	small

Variance evolutionary distinctiveness vs. phenotypic richness

res <- data %>% group_by(SEED, selection_name, problem_name) %>%
summarise(
  fit_phylo_10 = condinformation(discretize(max_performance), discretize(lag(variance_phenotype_evolutionary_distinctiveness, 1)), discretize(lag(max_performance, 1))),
  fit_phylo_100 = condinformation(discretize(max_performance), discretize(lag(variance_phenotype_evolutionary_distinctiveness, 10)), discretize(lag(max_performance, 10))),
  fit_phylo_1000 = condinformation(discretize(max_performance), discretize(lag(variance_phenotype_evolutionary_distinctiveness, 100)), discretize(lag(max_performance, 100))),
    fit_pheno_10 = condinformation(discretize(max_performance), discretize(lag(phenotype_num_taxa, 1)), discretize(lag(max_performance, 1))),
      fit_pheno_100 = condinformation(discretize(max_performance), discretize(lag(phenotype_num_taxa, 10)), discretize(lag(max_performance, 10))),
      fit_pheno_1000 = condinformation(discretize(max_performance), discretize(lag(phenotype_num_taxa, 100)), discretize(lag(max_performance, 100)))
      )

res <- res %>% pivot_longer(cols=contains("o_10"))
res$offset <- str_extract(res$name, "[:digit:]*$")
res$Type <- case_when(str_detect(res$name, "phylo") ~ "Phylogenetic", TRUE ~ "Phenotypic")

ggplot(
  res %>% filter(str_detect(name, "fit_ph*")), 
  aes(
    x=as.factor(offset), 
    y=value, 
    color=Type
    )
  ) + 
  geom_boxplot() + 
  facet_wrap(~selection_name*problem_name, ncol=4) + 
  scale_x_discrete("Lag") + 
  scale_y_continuous("Transfer Entropy") + 
  scale_color_discrete("") + 
  theme(legend.position = "bottom")

# Determine which conditions are significantly different from each other
transfer_entropy_stats(res)

selection_name	problem_name	offset	.y.	group1	group2	n1	n2	statistic	p	p.adj	p.adj.signif	label	effsize	magnitude
Eco-EA	Count Odds	10	value	Phenotypic	Phylogenetic	60	60	1719.0	0.673000	1.000000	ns	p = 1	0.0388098	small
Eco-EA	Count Odds	100	value	Phenotypic	Phylogenetic	60	60	1139.0	0.000527	0.031093		p = 0.031093	0.3167069	moderate
Eco-EA	Count Odds	1000	value	Phenotypic	Phylogenetic	60	60	1238.0	0.003210	0.189390	ns	p = 0.18939	0.2692821	small
Eco-EA	Logic-9	10	value	Phenotypic	Phylogenetic	60	60	1772.0	0.885000	1.000000	ns	p = 1	0.0134160	small
Eco-EA	Logic-9	100	value	Phenotypic	Phylogenetic	60	60	1278.0	0.006200	0.365800	ns	p = 0.3658	0.2501118	small
Eco-EA	Logic-9	1000	value	Phenotypic	Phylogenetic	60	60	1662.0	0.468000	1.000000	ns	p = 1	0.0664209	small
Eco-EA	NK Landscape	10	value	Phenotypic	Phylogenetic	60	60	1424.5	0.049000	1.000000	ns	p = 1	0.1799147	small
Eco-EA	NK Landscape	100	value	Phenotypic	Phylogenetic	60	60	1432.5	0.054100	1.000000	ns	p = 1	0.1760817	small
Eco-EA	NK Landscape	1000	value	Phenotypic	Phylogenetic	60	60	1560.0	0.209000	1.000000	ns	p = 1	0.1149939	small
Eco-EA	Sorting network	10	value	Phenotypic	Phylogenetic	60	60	1927.5	0.504000	1.000000	ns	p = 1	0.0611678	small
Eco-EA	Sorting network	100	value	Phenotypic	Phylogenetic	60	60	2162.5	0.057400	1.000000	ns	p = 1	0.1736866	small
Eco-EA	Sorting network	1000	value	Phenotypic	Phylogenetic	60	60	1799.0	0.993000	1.000000	ns	p = 1	0.0015407	small
Fitness sharing	Count Odds	10	value	Phenotypic	Phylogenetic	60	60	2113.0	0.101000	1.000000	ns	p = 1	0.1499686	small
Fitness sharing	Count Odds	100	value	Phenotypic	Phylogenetic	60	60	2054.0	0.183000	1.000000	ns	p = 1	0.1216998	small
Fitness sharing	Count Odds	1000	value	Phenotypic	Phylogenetic	60	60	1782.0	0.927000	1.000000	ns	p = 1	0.0086244	small
Fitness sharing	Logic-9	10	value	Phenotypic	Phylogenetic	60	60	1642.0	0.408000	1.000000	ns	p = 1	0.0757043	small
Fitness sharing	Logic-9	100	value	Phenotypic	Phylogenetic	60	60	1389.0	0.031200	1.000000	ns	p = 1	0.1969271	small
Fitness sharing	Logic-9	1000	value	Phenotypic	Phylogenetic	60	60	1639.0	0.398000	1.000000	ns	p = 1	0.0774129	small
Fitness sharing	NK Landscape	10	value	Phenotypic	Phylogenetic	60	60	1410.0	0.040900	1.000000	ns	p = 1	0.1868619	small
Fitness sharing	NK Landscape	100	value	Phenotypic	Phylogenetic	60	60	1304.0	0.009300	0.548700	ns	p = 0.5487	0.2376500	small
Fitness sharing	NK Landscape	1000	value	Phenotypic	Phylogenetic	60	60	1372.0	0.024800	1.000000	ns	p = 1	0.2050689	small
Fitness sharing	Sorting network	10	value	Phenotypic	Phylogenetic	60	60	1131.0	0.000450	0.026550		p = 0.02655	0.3205400	moderate
Fitness sharing	Sorting network	100	value	Phenotypic	Phylogenetic	60	60	2299.0	0.008890	0.524510	ns	p = 0.52451	0.2390874	small
Fitness sharing	Sorting network	1000	value	Phenotypic	Phylogenetic	60	60	1952.0	0.427000	1.000000	ns	p = 1	0.0728282	small
Lexicase	Count Odds	10	value	Phenotypic	Phylogenetic	60	60	1861.0	0.751000	1.000000	ns	p = 1	0.0292271	small
Lexicase	Count Odds	100	value	Phenotypic	Phylogenetic	60	60	1282.0	0.006600	0.389400	ns	p = 0.3894	0.2481909	small
Lexicase	Count Odds	1000	value	Phenotypic	Phylogenetic	60	60	1178.0	0.001110	0.065490	ns	p = 0.06549	0.2980207	small
Lexicase	Logic-9	10	value	Phenotypic	Phylogenetic	60	60	1705.5	0.622000	1.000000	ns	p = 1	0.0452781	small
Lexicase	Logic-9	100	value	Phenotypic	Phylogenetic	60	60	1334.0	0.014600	0.861400	ns	p = 0.8614	0.2232767	small
Lexicase	Logic-9	1000	value	Phenotypic	Phylogenetic	60	60	1697.0	0.589000	1.000000	ns	p = 1	0.0495490	small
Lexicase	NK Landscape	10	value	Phenotypic	Phylogenetic	60	60	1765.0	0.855000	1.000000	ns	p = 1	0.0168771	small
Lexicase	NK Landscape	100	value	Phenotypic	Phylogenetic	60	60	1576.0	0.238000	1.000000	ns	p = 1	0.1080132	small
Lexicase	NK Landscape	1000	value	Phenotypic	Phylogenetic	60	60	1346.0	0.016600	0.979400	ns	p = 0.9794	0.2189197	small
Lexicase	Sorting network	10	value	Phenotypic	Phylogenetic	60	60	1784.0	0.917000	1.000000	ns	p = 1	0.0098507	small
Lexicase	Sorting network	100	value	Phenotypic	Phylogenetic	60	60	1705.0	0.524000	1.000000	ns	p = 1	0.0584883	small
Random	Count Odds	10	value	Phenotypic	Phylogenetic	60	60	1721.0	0.680000	1.000000	ns	p = 1	0.0378515	small
Random	Count Odds	100	value	Phenotypic	Phylogenetic	60	60	1773.0	0.889000	1.000000	ns	p = 1	0.0129366	small
Random	Count Odds	1000	value	Phenotypic	Phylogenetic	60	60	1580.0	0.249000	1.000000	ns	p = 1	0.1054093	small
Random	Logic-9	10	value	Phenotypic	Phylogenetic	60	60	1728.0	0.672000	1.000000	ns	p = 1	0.0389639	small
Random	Logic-9	100	value	Phenotypic	Phylogenetic	60	60	1733.5	0.696000	1.000000	ns	p = 1	0.0359860	small
Random	Logic-9	1000	value	Phenotypic	Phylogenetic	60	60	1761.5	0.788000	1.000000	ns	p = 1	0.0248872	small
Random	NK Landscape	10	value	Phenotypic	Phylogenetic	60	60	1822.0	0.910000	1.000000	ns	p = 1	0.0105409	small
Random	NK Landscape	100	value	Phenotypic	Phylogenetic	60	60	1652.0	0.439000	1.000000	ns	p = 1	0.0709117	small
Random	NK Landscape	1000	value	Phenotypic	Phylogenetic	60	60	1587.0	0.265000	1.000000	ns	p = 1	0.1020553	small
Random	Sorting network	10	value	Phenotypic	Phylogenetic	60	60	2113.0	0.101000	1.000000	ns	p = 1	0.1499686	small
Random	Sorting network	100	value	Phenotypic	Phylogenetic	60	60	1629.0	0.371000	1.000000	ns	p = 1	0.0819317	small
Random	Sorting network	1000	value	Phenotypic	Phylogenetic	60	60	1852.0	0.787000	1.000000	ns	p = 1	0.0249149	small
Tournament	Count Odds	10	value	Phenotypic	Phylogenetic	60	60	1633.0	0.382000	1.000000	ns	p = 1	0.0800152	small
Tournament	Count Odds	100	value	Phenotypic	Phylogenetic	60	60	1153.0	0.000691	0.040769		p = 0.040769	0.3099990	moderate
Tournament	Count Odds	1000	value	Phenotypic	Phylogenetic	60	60	1599.5	0.294000	1.000000	ns	p = 1	0.0960720	small
Tournament	Logic-9	10	value	Phenotypic	Phylogenetic	60	60	1869.0	0.719000	1.000000	ns	p = 1	0.0330607	small
Tournament	Logic-9	100	value	Phenotypic	Phylogenetic	60	60	1284.0	0.006820	0.402380	ns	p = 0.40238	0.2472369	small
Tournament	Logic-9	1000	value	Phenotypic	Phylogenetic	60	60	1620.0	0.341000	1.000000	ns	p = 1	0.0871542	small
Tournament	NK Landscape	10	value	Phenotypic	Phylogenetic	60	60	1811.0	0.926000	1.000000	ns	p = 1	0.0089208	small
Tournament	NK Landscape	100	value	Phenotypic	Phylogenetic	60	60	1780.0	0.862000	1.000000	ns	p = 1	0.0162196	small
Tournament	NK Landscape	1000	value	Phenotypic	Phylogenetic	60	60	1775.0	0.828000	1.000000	ns	p = 1	0.0202745	small
Tournament	Sorting network	10	value	Phenotypic	Phylogenetic	60	60	1907.5	0.574000	1.000000	ns	p = 1	0.0515099	small
Tournament	Sorting network	100	value	Phenotypic	Phylogenetic	60	60	1287.0	0.007150	0.421850	ns	p = 0.42185	0.2457952	small
Tournament	Sorting network	1000	value	Phenotypic	Phylogenetic	60	60	1679.0	0.502000	1.000000	ns	p = 1	0.0615535	small

Transfer entropy between types of diversity

While we’re calculating transfer entropy, we might as well also calculate it between phenotypic diversity and phylogenetic diversity, as these could potentially also be in a feedback loop.

Max pairwise distance and phenotypic richness

res <- data %>% group_by(SEED, selection_name, problem_name) %>%
summarise(
  phen_phylo_10 =      condinformation(discretize(phenotype_num_taxa), 
                                       discretize(lag(max_phenotype_pairwise_distance, 1)), 
                                       discretize(lag(phenotype_num_taxa, 1))),
  phen_phylo_100 =     condinformation(discretize(phenotype_num_taxa),
                                       discretize(lag(max_phenotype_pairwise_distance, 10)),
                                       discretize(lag(phenotype_num_taxa, 10))),
  pheno_phylo_1000 =   condinformation(discretize(phenotype_num_taxa),
                                       discretize(lag(max_phenotype_pairwise_distance, 100)),
                                       discretize(lag(phenotype_num_taxa, 100))),
  
  phylo_pheno_10 =     condinformation(discretize(max_phenotype_pairwise_distance),
                                       discretize(lag(phenotype_num_taxa, 1)),
                                       discretize(lag(max_phenotype_pairwise_distance, 1))),
  phylo_pheno_100 =    condinformation(discretize(max_phenotype_pairwise_distance),
                                       discretize(lag(phenotype_num_taxa, 10)),
                                       discretize(lag(max_phenotype_pairwise_distance, 10))),
  phylo_pheno_1000 =   condinformation(discretize(max_phenotype_pairwise_distance),
                                       discretize(lag(phenotype_num_taxa, 100)),
                                       discretize(lag(max_phenotype_pairwise_distance, 100))))

# Turn Transfer Entropy columns into rows
res <- res %>% pivot_longer(cols=contains("phylo"))
# Pull lag into a column
res$offset <- str_extract(res$name, "[:digit:]*$")
# Make column indicating direction of transfer entropy
res$Type <- case_when(str_detect(res$name, "phylo_pheno") ~ "\nPhenotypic\n\t->\nPhylogenetic\n", TRUE ~ "\nPhylogenetic\n\t->\nPhenotypic\n")

ggplot(
  res, 
  aes(
    x=as.factor(offset), 
    y=value, 
    color=Type
    )
  ) + 
  geom_boxplot() + 
  facet_wrap(~selection_name* problem_name) + 
  scale_y_continuous("Transfer Entropy") + 
  scale_color_discrete("")

# Determine which conditions are significantly different from each other
transfer_entropy_stats(res)

selection_name	problem_name	offset	.y.	group1	group2	n1	n2	statistic	p	p.adj	p.adj.signif	label	effsize	magnitude
Eco-EA	Count Odds	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	13.0	0.00e+00	0.0000000	****	p < 1e-04	0.8562106	large
Eco-EA	Count Odds	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	223.0	0.00e+00	0.0000000	****	p < 1e-04	0.7555927	large
Eco-EA	Count Odds	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	855.0	7.00e-07	0.0000429	****	p < 1e-04	0.4527807	moderate
Eco-EA	Logic-9	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1931.0	4.93e-01	1.0000000	ns	p = 1	0.0627664	small
Eco-EA	Logic-9	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1919.0	5.34e-01	1.0000000	ns	p = 1	0.0570168	small
Eco-EA	Logic-9	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1910.0	5.65e-01	1.0000000	ns	p = 1	0.0527046	small
Eco-EA	NK Landscape	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	88.0	0.00e+00	0.0000000	****	p < 1e-04	0.8202757	large
Eco-EA	NK Landscape	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	601.0	0.00e+00	0.0000000	****	p < 1e-04	0.5744804	large
Eco-EA	NK Landscape	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1137.0	5.07e-04	0.0304200		p = 0.03042	0.3176652	moderate
Eco-EA	Sorting network	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	104.0	0.00e+00	0.0000000	****	p < 1e-04	0.8126095	large
Eco-EA	Sorting network	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	893.0	2.00e-06	0.0001176	***	p = 0.0001176	0.4345736	moderate
Eco-EA	Sorting network	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1533.0	1.62e-01	1.0000000	ns	p = 1	0.1279307	small
Fitness sharing	Count Odds	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	9.0	0.00e+00	0.0000000	****	p < 1e-04	0.8581272	large
Fitness sharing	Count Odds	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1754.0	8.11e-01	1.0000000	ns	p = 1	0.0220401	small
Fitness sharing	Count Odds	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1966.0	3.85e-01	1.0000000	ns	p = 1	0.0795361	small
Fitness sharing	Logic-9	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	661.0	0.00e+00	0.0000001	****	p < 1e-04	0.5457325	large
Fitness sharing	Logic-9	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	824.0	3.00e-07	0.0000183	****	p < 1e-04	0.4676338	moderate
Fitness sharing	Logic-9	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1273.0	5.72e-03	0.3432000	ns	p = 0.3432	0.2525031	small
Fitness sharing	NK Landscape	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	0.0	0.00e+00	0.0000000	****	p < 1e-04	0.8624394	large
Fitness sharing	NK Landscape	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	6.0	0.00e+00	0.0000000	****	p < 1e-04	0.8595646	large
Fitness sharing	NK Landscape	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	78.0	0.00e+00	0.0000000	****	p < 1e-04	0.8250670	large
Fitness sharing	Sorting network	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	13.0	0.00e+00	0.0000000	****	p < 1e-04	0.8562106	large
Fitness sharing	Sorting network	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2704.0	2.10e-06	0.0001266	***	p = 0.0001266	0.4331362	moderate
Fitness sharing	Sorting network	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2574.0	4.91e-05	0.0029460	**	p = 0.002946	0.3708489	moderate
Lexicase	Count Odds	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	0.0	0.00e+00	0.0000000	****	p < 1e-04	0.8624394	large
Lexicase	Count Odds	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	21.0	0.00e+00	0.0000000	****	p < 1e-04	0.8523776	large
Lexicase	Count Odds	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	450.0	0.00e+00	0.0000000	****	p < 1e-04	0.6468295	large
Lexicase	Logic-9	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1406.0	3.89e-02	1.0000000	ns	p = 1	0.1887784	small
Lexicase	Logic-9	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1553.0	1.96e-01	1.0000000	ns	p = 1	0.1183458	small
Lexicase	Logic-9	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1409.0	4.04e-02	1.0000000	ns	p = 1	0.1873410	small
Lexicase	NK Landscape	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	0.0	0.00e+00	0.0000000	****	p < 1e-04	0.8624394	large
Lexicase	NK Landscape	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	0.0	0.00e+00	0.0000000	****	p < 1e-04	0.8624394	large
Lexicase	NK Landscape	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	8.0	0.00e+00	0.0000000	****	p < 1e-04	0.8586063	large
Lexicase	Sorting network	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	62.0	0.00e+00	0.0000000	****	p < 1e-04	0.8327331	large
Lexicase	Sorting network	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	239.0	0.00e+00	0.0000000	****	p < 1e-04	0.7479266	large
Lexicase	Sorting network	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	30.0	0.00e+00	0.0000000	****	p < 1e-04	0.9099165	large
Random	Count Odds	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	0.0	0.00e+00	0.0000000	****	p < 1e-04	0.8624394	large
Random	Count Odds	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	12.0	0.00e+00	0.0000000	****	p < 1e-04	0.8566898	large
Random	Count Odds	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	61.0	0.00e+00	0.0000000	****	p < 1e-04	0.8332123	large
Random	Logic-9	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	327.0	0.00e+00	0.0000000	****	p < 1e-04	0.7057629	large
Random	Logic-9	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	924.0	4.30e-06	0.0002592	***	p = 0.0002592	0.4197205	moderate
Random	Logic-9	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1283.0	6.71e-03	0.4026000	ns	p = 0.4026	0.2477118	small
Random	NK Landscape	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	0.0	0.00e+00	0.0000000	****	p < 1e-04	0.8624394	large
Random	NK Landscape	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	0.0	0.00e+00	0.0000000	****	p < 1e-04	0.8624394	large
Random	NK Landscape	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	40.0	0.00e+00	0.0000000	****	p < 1e-04	0.8432740	large
Random	Sorting network	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	155.0	0.00e+00	0.0000000	****	p < 1e-04	0.7881738	large
Random	Sorting network	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	212.0	0.00e+00	0.0000000	****	p < 1e-04	0.7608632	large
Random	Sorting network	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	126.0	0.00e+00	0.0000000	****	p < 1e-04	0.8020686	large
Tournament	Count Odds	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1761.0	8.40e-01	1.0000000	ns	p = 1	0.0186862	small
Tournament	Count Odds	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2479.0	3.69e-04	0.0221400		p = 0.02214	0.3253313	moderate
Tournament	Count Odds	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2207.0	3.29e-02	1.0000000	ns	p = 1	0.1950071	small
Tournament	Logic-9	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2835.0	1.00e-07	0.0000034	****	p < 1e-04	0.4959026	moderate
Tournament	Logic-9	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2802.0	1.00e-07	0.0000088	****	p < 1e-04	0.4800912	moderate
Tournament	Logic-9	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2201.5	3.53e-02	1.0000000	ns	p = 1	0.1923752	small
Tournament	NK Landscape	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	308.0	0.00e+00	0.0000000	****	p < 1e-04	0.7148664	large
Tournament	NK Landscape	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	682.0	0.00e+00	0.0000003	****	p < 1e-04	0.5356707	large
Tournament	NK Landscape	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1216.5	2.21e-03	0.1326000	ns	p = 0.1326	0.2795746	small
Tournament	Sorting network	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	586.0	0.00e+00	0.0000000	****	p < 1e-04	0.5816674	large
Tournament	Sorting network	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1292.0	7.73e-03	0.4638000	ns	p = 0.4638	0.2433996	small
Tournament	Sorting network	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1090.5	1.98e-04	0.0118800		p = 0.01188	0.3399454	moderate

Mean pairwise distance and phenotypic richness

res <- data %>% group_by(SEED, selection_name, problem_name) %>%
summarise(
  phen_phylo_10 =      condinformation(discretize(phenotype_num_taxa), 
                                       discretize(lag(mean_phenotype_pairwise_distance, 1)), 
                                       discretize(lag(phenotype_num_taxa, 1))),
  phen_phylo_100 =     condinformation(discretize(phenotype_num_taxa),
                                       discretize(lag(mean_phenotype_pairwise_distance, 10)),
                                       discretize(lag(phenotype_num_taxa, 10))),
  pheno_phylo_1000 =   condinformation(discretize(phenotype_num_taxa),
                                       discretize(lag(mean_phenotype_pairwise_distance, 100)),
                                       discretize(lag(phenotype_num_taxa, 100))),
  
  phylo_pheno_10 =     condinformation(discretize(mean_phenotype_pairwise_distance),
                                       discretize(lag(phenotype_num_taxa, 1)),
                                       discretize(lag(mean_phenotype_pairwise_distance, 1))),
  phylo_pheno_100 =    condinformation(discretize(mean_phenotype_pairwise_distance),
                                       discretize(lag(phenotype_num_taxa, 10)),
                                       discretize(lag(mean_phenotype_pairwise_distance, 10))),
  phylo_pheno_1000 =   condinformation(discretize(mean_phenotype_pairwise_distance),
                                       discretize(lag(phenotype_num_taxa, 100)),
                                       discretize(lag(mean_phenotype_pairwise_distance, 100)))
)

# Turn Transfer Entropy columns into rows
res <- res %>% pivot_longer(cols=contains("phylo"))
# Pull lag into a column
res$offset <- str_extract(res$name, "[:digit:]*$")
# Make column indicating direction of transfer entropy
res$Type <- case_when(str_detect(res$name, "phylo_pheno") ~ "\nPhenotypic\n\t->\nPhylogenetic\n", TRUE ~ "\nPhylogenetic\n\t->\nPhenotypic\n")

ggplot(
  res, 
  aes(
    x=as.factor(offset), 
    y=value, 
    color=Type
    )
  ) + 
  geom_boxplot() + 
  facet_wrap(~selection_name*problem_name, ncol=4) + 
  scale_y_continuous("Transfer Entropy") + 
  scale_color_discrete("")

# Determine which conditions are significantly different from each other
transfer_entropy_stats(res)

selection_name	problem_name	offset	.y.	group1	group2	n1	n2	statistic	p	p.adj	p.adj.signif	label	effsize	magnitude
Eco-EA	Count Odds	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	293.0	0.00e+00	0.0000000	****	p < 1e-04	0.7220534	large
Eco-EA	Count Odds	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	786.0	1.00e-07	0.0000062	****	p < 1e-04	0.4858408	moderate
Eco-EA	Count Odds	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1136.0	4.97e-04	0.0298200		p = 0.02982	0.3181443	moderate
Eco-EA	Logic-9	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1358.0	2.05e-02	1.0000000	ns	p = 1	0.2117768	small
Eco-EA	Logic-9	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1973.0	3.65e-01	1.0000000	ns	p = 1	0.0828900	small
Eco-EA	Logic-9	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1729.0	7.11e-01	1.0000000	ns	p = 1	0.0340184	small
Eco-EA	NK Landscape	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	103.0	0.00e+00	0.0000000	****	p < 1e-04	0.8130887	large
Eco-EA	NK Landscape	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	929.0	4.90e-06	0.0002940	***	p = 0.000294	0.4173248	moderate
Eco-EA	NK Landscape	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1215.0	2.16e-03	0.1296000	ns	p = 0.1296	0.2802928	small
Eco-EA	Sorting network	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	63.0	0.00e+00	0.0000000	****	p < 1e-04	0.8322540	large
Eco-EA	Sorting network	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	798.0	1.00e-07	0.0000088	****	p < 1e-04	0.4800912	moderate
Eco-EA	Sorting network	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1946.0	4.45e-01	1.0000000	ns	p = 1	0.0699546	small
Fitness sharing	Count Odds	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	8.0	0.00e+00	0.0000000	****	p < 1e-04	0.8586063	large
Fitness sharing	Count Odds	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1961.0	4.00e-01	1.0000000	ns	p = 1	0.0771404	small
Fitness sharing	Count Odds	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1984.0	3.35e-01	1.0000000	ns	p = 1	0.0881605	small
Fitness sharing	Logic-9	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	595.0	0.00e+00	0.0000000	****	p < 1e-04	0.5773552	large
Fitness sharing	Logic-9	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	884.0	1.60e-06	0.0000930	****	p < 1e-04	0.4388858	moderate
Fitness sharing	Logic-9	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	807.0	2.00e-07	0.0000114	****	p < 1e-04	0.4757790	moderate
Fitness sharing	NK Landscape	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	0.0	0.00e+00	0.0000000	****	p < 1e-04	0.8624394	large
Fitness sharing	NK Landscape	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	66.0	0.00e+00	0.0000000	****	p < 1e-04	0.8308166	large
Fitness sharing	NK Landscape	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	339.0	0.00e+00	0.0000000	****	p < 1e-04	0.7000133	large
Fitness sharing	Sorting network	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	18.0	0.00e+00	0.0000000	****	p < 1e-04	0.8538150	large
Fitness sharing	Sorting network	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2969.0	0.00e+00	0.0000001	****	p < 1e-04	0.5601065	large
Fitness sharing	Sorting network	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2214.0	3.00e-02	1.0000000	ns	p = 1	0.1983611	small
Lexicase	Count Odds	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1.0	0.00e+00	0.0000000	****	p < 1e-04	0.8619602	large
Lexicase	Count Odds	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	91.0	0.00e+00	0.0000000	****	p < 1e-04	0.8188383	large
Lexicase	Count Odds	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	766.0	1.00e-07	0.0000035	****	p < 1e-04	0.4954235	moderate
Lexicase	Logic-9	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1790.0	9.60e-01	1.0000000	ns	p = 1	0.0047913	small
Lexicase	Logic-9	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1782.0	9.27e-01	1.0000000	ns	p = 1	0.0086244	small
Lexicase	Logic-9	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1499.0	1.15e-01	1.0000000	ns	p = 1	0.1442190	small
Lexicase	NK Landscape	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	0.0	0.00e+00	0.0000000	****	p < 1e-04	0.8624394	large
Lexicase	NK Landscape	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	0.0	0.00e+00	0.0000000	****	p < 1e-04	0.8624394	large
Lexicase	NK Landscape	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	5.0	0.00e+00	0.0000000	****	p < 1e-04	0.8600452	large
Lexicase	Sorting network	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1354.0	1.87e-02	1.0000000	ns	p = 1	0.2149192	small
Lexicase	Sorting network	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1484.0	9.64e-02	1.0000000	ns	p = 1	0.1520143	small
Lexicase	Sorting network	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1646.0	4.20e-01	1.0000000	ns	p = 1	0.0738231	small
Random	Count Odds	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1.0	0.00e+00	0.0000000	****	p < 1e-04	0.8619602	large
Random	Count Odds	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	45.0	0.00e+00	0.0000000	****	p < 1e-04	0.8408784	large
Random	Count Odds	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	286.0	0.00e+00	0.0000000	****	p < 1e-04	0.7254073	large
Random	Logic-9	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	540.0	0.00e+00	0.0000000	****	p < 1e-04	0.6037076	large
Random	Logic-9	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1017.0	4.01e-05	0.0024060	**	p = 0.002406	0.3751611	moderate
Random	Logic-9	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	903.0	2.50e-06	0.0001518	***	p = 0.0001518	0.4297823	moderate
Random	NK Landscape	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	0.0	0.00e+00	0.0000000	****	p < 1e-04	0.8624394	large
Random	NK Landscape	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	37.0	0.00e+00	0.0000000	****	p < 1e-04	0.8447114	large
Random	NK Landscape	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	303.0	0.00e+00	0.0000000	****	p < 1e-04	0.7172621	large
Random	Sorting network	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	296.0	0.00e+00	0.0000000	****	p < 1e-04	0.7206160	large
Random	Sorting network	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	439.0	0.00e+00	0.0000000	****	p < 1e-04	0.6521000	large
Random	Sorting network	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	258.0	0.00e+00	0.0000000	****	p < 1e-04	0.7388231	large
Tournament	Count Odds	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	897.0	2.20e-06	0.0001302	***	p = 0.0001302	0.4326571	moderate
Tournament	Count Odds	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2506.0	2.13e-04	0.0127800		p = 0.01278	0.3382679	moderate
Tournament	Count Odds	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2557.0	7.17e-05	0.0043020	**	p = 0.004302	0.3627043	moderate
Tournament	Logic-9	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1086.0	1.80e-04	0.0108000		p = 0.0108	0.3421009	moderate
Tournament	Logic-9	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2600.0	2.71e-05	0.0016260	**	p = 0.001626	0.3833064	moderate
Tournament	Logic-9	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1995.0	3.07e-01	1.0000000	ns	p = 1	0.0934309	small
Tournament	NK Landscape	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	317.0	0.00e+00	0.0000000	****	p < 1e-04	0.7105542	large
Tournament	NK Landscape	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	951.0	8.50e-06	0.0005070	***	p = 0.000507	0.4067839	moderate
Tournament	NK Landscape	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1450.0	6.66e-02	1.0000000	ns	p = 1	0.1676977	small
Tournament	Sorting network	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	259.0	0.00e+00	0.0000000	****	p < 1e-04	0.7383439	large
Tournament	Sorting network	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1489.0	1.03e-01	1.0000000	ns	p = 1	0.1490104	small
Tournament	Sorting network	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1485.5	9.93e-02	1.0000000	ns	p = 1	0.1506876	small

Mean pairwise distance and shannon diversity

res <- data %>% group_by(SEED, selection_name, problem_name) %>%
summarise(
  phen_phylo_10 =      condinformation(discretize(phenotype_diversity), 
                                       discretize(lag(mean_phenotype_pairwise_distance, 1)), 
                                       discretize(lag(phenotype_diversity, 1))),
  phen_phylo_100 =     condinformation(discretize(phenotype_diversity),
                                       discretize(lag(mean_phenotype_pairwise_distance, 10)),
                                       discretize(lag(phenotype_diversity, 10))),
  pheno_phylo_1000 =   condinformation(discretize(phenotype_diversity),
                                       discretize(lag(mean_phenotype_pairwise_distance, 100)),
                                       discretize(lag(phenotype_diversity, 100))),
  phylo_pheno_10 =     condinformation(discretize(mean_phenotype_pairwise_distance),
                                       discretize(lag(phenotype_diversity, 1)),
                                       discretize(lag(mean_phenotype_pairwise_distance, 1))),
  phylo_pheno_100 =    condinformation(discretize(mean_phenotype_pairwise_distance),
                                       discretize(lag(phenotype_diversity, 10)),
                                       discretize(lag(mean_phenotype_pairwise_distance, 10))),
  phylo_pheno_1000 =   condinformation(discretize(mean_phenotype_pairwise_distance),
                                       discretize(lag(phenotype_diversity, 100)),
                                       discretize(lag(mean_phenotype_pairwise_distance, 100)))
  
)

# Turn Transfer Entropy columns into rows
res <- res %>% pivot_longer(cols=contains("phylo"))
# Pull lag into a column
res$offset <- str_extract(res$name, "[:digit:]*$")
# Make column indicating direction of transfer entropy
res$Type <- case_when(str_detect(res$name, "phylo_pheno") ~ "\nPhenotypic\n\t->\nPhylogenetic\n", TRUE ~ "\nPhylogenetic\n\t->\nPhenotypic\n")

ggplot(
  res, 
  aes(
    x=as.factor(offset), 
    y=value, 
    color=Type
    )
  ) + 
  geom_boxplot() + 
  facet_wrap(~selection_name*problem_name, ncol=4) + 
  scale_y_continuous("Transfer Entropy") + 
  scale_color_discrete("")

# Determine which conditions are significantly different from each other
transfer_entropy_stats(res)

selection_name	problem_name	offset	.y.	group1	group2	n1	n2	statistic	p	p.adj	p.adj.signif	label	effsize	magnitude
Eco-EA	Count Odds	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	690	0.00e+00	0.0000003	****	p < 1e-04	0.5318376	large
Eco-EA	Count Odds	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	879	1.40e-06	0.0000816	****	p < 1e-04	0.4412815	moderate
Eco-EA	Count Odds	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	942	6.80e-06	0.0004062	***	p = 0.0004062	0.4110961	moderate
Eco-EA	Logic-9	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1281	6.50e-03	0.3900000	ns	p = 0.39	0.2486700	small
Eco-EA	Logic-9	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1816	9.35e-01	1.0000000	ns	p = 1	0.0076661	small
Eco-EA	Logic-9	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1347	1.75e-02	1.0000000	ns	p = 1	0.2170472	small
Eco-EA	NK Landscape	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1125	4.00e-04	0.0240000		p = 0.024	0.3234148	moderate
Eco-EA	NK Landscape	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1207	1.87e-03	0.1122000	ns	p = 0.1122	0.2841259	small
Eco-EA	NK Landscape	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1488	1.02e-01	1.0000000	ns	p = 1	0.1494895	small
Eco-EA	Sorting network	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	485	0.00e+00	0.0000000	****	p < 1e-04	0.6300599	large
Eco-EA	Sorting network	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2799	2.00e-07	0.0000096	****	p < 1e-04	0.4786538	moderate
Eco-EA	Sorting network	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2342	4.48e-03	0.2688000	ns	p = 0.2688	0.2596905	small
Fitness sharing	Count Odds	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	6	0.00e+00	0.0000000	****	p < 1e-04	0.8595646	large
Fitness sharing	Count Odds	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1853	7.83e-01	1.0000000	ns	p = 1	0.0253940	small
Fitness sharing	Count Odds	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1953	4.23e-01	1.0000000	ns	p = 1	0.0733073	small
Fitness sharing	Logic-9	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	678	0.00e+00	0.0000002	****	p < 1e-04	0.5375872	large
Fitness sharing	Logic-9	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	913	3.30e-06	0.0001962	***	p = 0.0001962	0.4249910	moderate
Fitness sharing	Logic-9	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	838	4.00e-07	0.0000270	****	p < 1e-04	0.4609259	moderate
Fitness sharing	NK Landscape	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	0	0.00e+00	0.0000000	****	p < 1e-04	0.8624394	large
Fitness sharing	NK Landscape	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	66	0.00e+00	0.0000000	****	p < 1e-04	0.8308166	large
Fitness sharing	NK Landscape	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	323	0.00e+00	0.0000000	****	p < 1e-04	0.7076794	large
Fitness sharing	Sorting network	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	35	0.00e+00	0.0000000	****	p < 1e-04	0.8456697	large
Fitness sharing	Sorting network	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2967	0.00e+00	0.0000001	****	p < 1e-04	0.5591482	large
Fitness sharing	Sorting network	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2361	3.26e-03	0.1956000	ns	p = 0.1956	0.2687936	small
Lexicase	Count Odds	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1	0.00e+00	0.0000000	****	p < 1e-04	0.8619602	large
Lexicase	Count Odds	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	105	0.00e+00	0.0000000	****	p < 1e-04	0.8121304	large
Lexicase	Count Odds	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	803	2.00e-07	0.0000101	****	p < 1e-04	0.4776956	moderate
Lexicase	Logic-9	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1925	5.13e-01	1.0000000	ns	p = 1	0.0598916	small
Lexicase	Logic-9	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2036	2.16e-01	1.0000000	ns	p = 1	0.1130754	small
Lexicase	Logic-9	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1509	1.27e-01	1.0000000	ns	p = 1	0.1394277	small
Lexicase	NK Landscape	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	0	0.00e+00	0.0000000	****	p < 1e-04	0.8624394	large
Lexicase	NK Landscape	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	0	0.00e+00	0.0000000	****	p < 1e-04	0.8624394	large
Lexicase	NK Landscape	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1	0.00e+00	0.0000000	****	p < 1e-04	0.8619602	large
Lexicase	Sorting network	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1837	8.08e-01	1.0000000	ns	p = 1	0.0225336	small
Lexicase	Sorting network	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1781	9.04e-01	1.0000000	ns	p = 1	0.0113385	small
Lexicase	Sorting network	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1551	1.89e-01	1.0000000	ns	p = 1	0.1201541	small
Random	Count Odds	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	0	0.00e+00	0.0000000	****	p < 1e-04	0.8624394	large
Random	Count Odds	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	69	0.00e+00	0.0000000	****	p < 1e-04	0.8293792	large
Random	Count Odds	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	238	0.00e+00	0.0000000	****	p < 1e-04	0.7484057	large
Random	Logic-9	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	3339	0.00e+00	0.0000000	****	p < 1e-04	0.7373857	large
Random	Logic-9	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2603	2.53e-05	0.0015180	**	p = 0.001518	0.3847438	moderate
Random	Logic-9	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1823	9.06e-01	1.0000000	ns	p = 1	0.0110201	small
Random	NK Landscape	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	0	0.00e+00	0.0000000	****	p < 1e-04	0.8624394	large
Random	NK Landscape	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	50	0.00e+00	0.0000000	****	p < 1e-04	0.8384827	large
Random	NK Landscape	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	290	0.00e+00	0.0000000	****	p < 1e-04	0.7234908	large
Random	Sorting network	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	593	0.00e+00	0.0000000	****	p < 1e-04	0.5783135	large
Random	Sorting network	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	354	0.00e+00	0.0000000	****	p < 1e-04	0.6928263	large
Random	Sorting network	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	323	0.00e+00	0.0000000	****	p < 1e-04	0.7076794	large
Tournament	Count Odds	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2170	5.25e-02	1.0000000	ns	p = 1	0.1772792	small
Tournament	Count Odds	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2383	2.23e-03	0.1338000	ns	p = 0.1338	0.2793345	small
Tournament	Count Odds	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2165	5.57e-02	1.0000000	ns	p = 1	0.1748848	small
Tournament	Logic-9	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1703	6.13e-01	1.0000000	ns	p = 1	0.0464759	small
Tournament	Logic-9	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2327	5.72e-03	0.3432000	ns	p = 0.3432	0.2525031	small
Tournament	Logic-9	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1477	9.05e-02	1.0000000	ns	p = 1	0.1547600	small
Tournament	NK Landscape	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1401	3.65e-02	1.0000000	ns	p = 1	0.1911741	small
Tournament	NK Landscape	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1809	9.64e-01	1.0000000	ns	p = 1	0.0043122	small
Tournament	NK Landscape	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1939	4.67e-01	1.0000000	ns	p = 1	0.0665999	small
Tournament	Sorting network	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	612	0.00e+00	0.0000000	****	p < 1e-04	0.5692100	large
Tournament	Sorting network	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1154	7.04e-04	0.0422400		p = 0.04224	0.3095199	moderate
Tournament	Sorting network	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1497	1.12e-01	1.0000000	ns	p = 1	0.1451773	small

Mean evolutionary distinctiveness and phenotypic richness

res <- data %>% group_by(SEED, selection_name, problem_name) %>%
summarise(
  phen_phylo_10 =      condinformation(
                          discretize(phenotype_num_taxa), 
                          discretize(lag(mean_phenotype_evolutionary_distinctiveness, 1)), 
                          discretize(lag(phenotype_num_taxa, 1))),
  phen_phylo_100 =     condinformation(
                          discretize(phenotype_num_taxa),
                          discretize(lag(mean_phenotype_evolutionary_distinctiveness, 10)),
                          discretize(lag(phenotype_num_taxa, 10))),
  pheno_phylo_1000 =   condinformation(
                          discretize(phenotype_num_taxa),
                          discretize(lag(mean_phenotype_evolutionary_distinctiveness, 100)),
                          discretize(lag(phenotype_num_taxa, 100))),
  
  phylo_pheno_10 =     condinformation(
                          discretize(mean_phenotype_evolutionary_distinctiveness),
                          discretize(lag(phenotype_num_taxa, 1)),
                          discretize(lag(mean_phenotype_evolutionary_distinctiveness, 1))),
  phylo_pheno_100 =    condinformation(
                          discretize(mean_phenotype_evolutionary_distinctiveness),
                          discretize(lag(phenotype_num_taxa, 10)),
                          discretize(lag(mean_phenotype_evolutionary_distinctiveness, 10))),
  phylo_pheno_1000 =   condinformation(
                          discretize(mean_phenotype_evolutionary_distinctiveness),
                          discretize(lag(phenotype_num_taxa, 100)),
                          discretize(lag(mean_phenotype_evolutionary_distinctiveness, 100)))
)

# Turn Transfer Entropy columns into rows
res <- res %>% pivot_longer(cols=contains("phylo"))
# Pull lag into a column
res$offset <- str_extract(res$name, "[:digit:]*$")
# Make column indicating direction of transfer entropy
res$Type <- case_when(str_detect(res$name, "phylo_pheno") ~ "\nPhenotypic\n\t->\nPhylogenetic\n", TRUE ~ "\nPhylogenetic\n\t->\nPhenotypic\n")

ggplot(
  res, 
  aes(
    x=as.factor(offset), 
    y=value, 
    color=Type
    )
  ) + 
  geom_boxplot() + 
  facet_wrap(~selection_name*problem_name, ncol=4) + 
  scale_y_continuous("Transfer Entropy") +  
  scale_color_discrete("")

# Determine which conditions are significantly different from each other
transfer_entropy_stats(res)

selection_name	problem_name	offset	.y.	group1	group2	n1	n2	statistic	p	p.adj	p.adj.signif	label	effsize	magnitude
Eco-EA	Count Odds	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	208	0.00e+00	0.0000000	****	p < 1e-04	0.7627797	large
Eco-EA	Count Odds	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1150	6.52e-04	0.0391200		p = 0.03912	0.3114364	moderate
Eco-EA	Count Odds	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1525	1.50e-01	1.0000000	ns	p = 1	0.1317616	small
Eco-EA	Logic-9	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	58	0.00e+00	0.0000000	****	p < 1e-04	0.8346496	large
Eco-EA	Logic-9	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1069	1.26e-04	0.0075600	**	p = 0.00756	0.3502462	moderate
Eco-EA	Logic-9	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1944	4.51e-01	1.0000000	ns	p = 1	0.0689951	small
Eco-EA	NK Landscape	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1	0.00e+00	0.0000000	****	p < 1e-04	0.8619602	large
Eco-EA	NK Landscape	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	204	0.00e+00	0.0000000	****	p < 1e-04	0.7646962	large
Eco-EA	NK Landscape	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	485	0.00e+00	0.0000000	****	p < 1e-04	0.6300599	large
Eco-EA	Sorting network	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	0	0.00e+00	0.0000000	****	p < 1e-04	0.8624394	large
Eco-EA	Sorting network	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	0	0.00e+00	0.0000000	****	p < 1e-04	0.8624394	large
Eco-EA	Sorting network	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	155	0.00e+00	0.0000000	****	p < 1e-04	0.7881751	large
Fitness sharing	Count Odds	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	453	0.00e+00	0.0000000	****	p < 1e-04	0.6453921	large
Fitness sharing	Count Odds	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1894	6.24e-01	1.0000000	ns	p = 1	0.0450385	small
Fitness sharing	Count Odds	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2181	4.58e-02	1.0000000	ns	p = 1	0.1825497	small
Fitness sharing	Logic-9	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1024	4.69e-05	0.0028140	**	p = 0.002814	0.3718072	moderate
Fitness sharing	Logic-9	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2288	1.05e-02	0.6300000	ns	p = 0.63	0.2338169	small
Fitness sharing	Logic-9	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2254	1.73e-02	1.0000000	ns	p = 1	0.2175264	small
Fitness sharing	NK Landscape	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	106	0.00e+00	0.0000000	****	p < 1e-04	0.8116513	large
Fitness sharing	NK Landscape	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	603	0.00e+00	0.0000000	****	p < 1e-04	0.5735222	large
Fitness sharing	NK Landscape	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	823	3.00e-07	0.0000178	****	p < 1e-04	0.4681129	moderate
Fitness sharing	Sorting network	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2320	6.40e-03	0.3840000	ns	p = 0.384	0.2491491	small
Fitness sharing	Sorting network	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	3370	0.00e+00	0.0000000	****	p < 1e-04	0.7522388	large
Fitness sharing	Sorting network	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	3170	0.00e+00	0.0000000	****	p < 1e-04	0.6564167	large
Lexicase	Count Odds	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	6	0.00e+00	0.0000000	****	p < 1e-04	0.8595646	large
Lexicase	Count Odds	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	128	0.00e+00	0.0000000	****	p < 1e-04	0.8011103	large
Lexicase	Count Odds	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	801	2.00e-07	0.0000096	****	p < 1e-04	0.4786538	moderate
Lexicase	Logic-9	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	876	1.30e-06	0.0000750	****	p < 1e-04	0.4427189	moderate
Lexicase	Logic-9	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1975	3.60e-01	1.0000000	ns	p = 1	0.0838483	small
Lexicase	Logic-9	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2664	5.80e-06	0.0003504	***	p = 0.0003504	0.4139716	moderate
Lexicase	NK Landscape	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	10	0.00e+00	0.0000000	****	p < 1e-04	0.8576480	large
Lexicase	NK Landscape	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	26	0.00e+00	0.0000000	****	p < 1e-04	0.8499819	large
Lexicase	NK Landscape	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	67	0.00e+00	0.0000000	****	p < 1e-04	0.8303375	large
Lexicase	Sorting network	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	0	0.00e+00	0.0000000	****	p < 1e-04	0.8624409	large
Lexicase	Sorting network	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	0	0.00e+00	0.0000000	****	p < 1e-04	0.8624394	large
Lexicase	Sorting network	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	67	0.00e+00	0.0000000	****	p < 1e-04	0.8303389	large
Random	Count Odds	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	285	0.00e+00	0.0000000	****	p < 1e-04	0.7258865	large
Random	Count Odds	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	995	2.42e-05	0.0014520	**	p = 0.001452	0.3857020	moderate
Random	Count Odds	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1148	6.27e-04	0.0376200		p = 0.03762	0.3123947	moderate
Random	Logic-9	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	159	0.00e+00	0.0000000	****	p < 1e-04	0.7862572	large
Random	Logic-9	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	790	1.00e-07	0.0000070	****	p < 1e-04	0.4839243	moderate
Random	Logic-9	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	650	0.00e+00	0.0000001	****	p < 1e-04	0.5510029	large
Random	NK Landscape	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	94	0.00e+00	0.0000000	****	p < 1e-04	0.8174009	large
Random	NK Landscape	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	439	0.00e+00	0.0000000	****	p < 1e-04	0.6521000	large
Random	NK Landscape	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	683	0.00e+00	0.0000003	****	p < 1e-04	0.5351915	large
Random	Sorting network	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1649	4.30e-01	1.0000000	ns	p = 1	0.0723491	small
Random	Sorting network	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1652	4.39e-01	1.0000000	ns	p = 1	0.0709117	small
Random	Sorting network	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2051	1.89e-01	1.0000000	ns	p = 1	0.1202624	small
Tournament	Count Odds	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	339	0.00e+00	0.0000000	****	p < 1e-04	0.7000133	large
Tournament	Count Odds	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2222	2.69e-02	1.0000000	ns	p = 1	0.2021941	small
Tournament	Count Odds	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2166	5.51e-02	1.0000000	ns	p = 1	0.1753627	small
Tournament	Logic-9	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	0	0.00e+00	0.0000000	****	p < 1e-04	0.8624394	large
Tournament	Logic-9	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	491	0.00e+00	0.0000000	****	p < 1e-04	0.6271851	large
Tournament	Logic-9	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1873	7.04e-01	1.0000000	ns	p = 1	0.0349767	small
Tournament	NK Landscape	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	0	0.00e+00	0.0000000	****	p < 1e-04	0.8624394	large
Tournament	NK Landscape	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1	0.00e+00	0.0000000	****	p < 1e-04	0.8619602	large
Tournament	NK Landscape	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	25	0.00e+00	0.0000000	****	p < 1e-04	0.8504640	large
Tournament	Sorting network	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	4	0.00e+00	0.0000000	****	p < 1e-04	0.8605228	large
Tournament	Sorting network	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	69	0.00e+00	0.0000000	****	p < 1e-04	0.8293792	large
Tournament	Sorting network	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	357	0.00e+00	0.0000000	****	p < 1e-04	0.6913889	large

Mean evolutionary distinctiveness and shannon diversity

res <- data %>% group_by(SEED, selection_name, problem_name) %>%
summarise(
  phen_phylo_10 =      condinformation(
                          discretize(phenotype_diversity), 
                          discretize(lag(mean_phenotype_evolutionary_distinctiveness, 1)), 
                          discretize(lag(phenotype_diversity, 1))),
  phen_phylo_100 =     condinformation(
                          discretize(phenotype_diversity),
                          discretize(lag(mean_phenotype_evolutionary_distinctiveness, 10)),
                          discretize(lag(phenotype_diversity, 10))),
  pheno_phylo_1000 =   condinformation(
                          discretize(phenotype_diversity),
                          discretize(lag(mean_phenotype_evolutionary_distinctiveness, 100)),
                          discretize(lag(phenotype_diversity, 100))),
  
  phylo_pheno_10 =     condinformation(
                          discretize(mean_phenotype_evolutionary_distinctiveness),
                          discretize(lag(phenotype_diversity, 1)),
                          discretize(lag(mean_phenotype_evolutionary_distinctiveness, 1))),
  phylo_pheno_100 =    condinformation(
                          discretize(mean_phenotype_evolutionary_distinctiveness),
                          discretize(lag(phenotype_diversity, 10)),
                          discretize(lag(mean_phenotype_evolutionary_distinctiveness, 10))),
  phylo_pheno_1000 =   condinformation(
                          discretize(mean_phenotype_evolutionary_distinctiveness),
                          discretize(lag(phenotype_diversity, 100)),
                          discretize(lag(mean_phenotype_evolutionary_distinctiveness, 100)))
)

# Turn Transfer Entropy columns into rows
res <- res %>% pivot_longer(cols=contains("phylo"))
# Pull lag into a column
res$offset <- str_extract(res$name, "[:digit:]*$")
# Make column indicating direction of transfer entropy
res$Type <- case_when(str_detect(res$name, "phylo_pheno") ~ "\nPhenotypic\n\t->\nPhylogenetic\n", TRUE ~ "\nPhylogenetic\n\t->\nPhenotypic\n")

ggplot(
  res, 
  aes(
    x=as.factor(offset), 
    y=value, 
    color=Type
    )
  ) + 
  geom_boxplot() + 
  facet_wrap(~selection_name*problem_name, ncol=4) + 
  scale_y_continuous("Transfer Entropy") + 
  scale_color_discrete("")

# Determine which conditions are significantly different from each other
transfer_entropy_stats(res)

selection_name	problem_name	offset	.y.	group1	group2	n1	n2	statistic	p	p.adj	p.adj.signif	label	effsize	magnitude
Eco-EA	Count Odds	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	565.0	0.00e+00	0.0000000	****	p < 1e-04	0.5917292	large
Eco-EA	Count Odds	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1273.0	5.72e-03	0.3432000	ns	p = 0.3432	0.2525031	small
Eco-EA	Count Odds	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1148.0	6.27e-04	0.0376200		p = 0.03762	0.3123947	moderate
Eco-EA	Logic-9	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	67.0	0.00e+00	0.0000000	****	p < 1e-04	0.8303375	large
Eco-EA	Logic-9	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1078.0	1.53e-04	0.0091800	**	p = 0.00918	0.3459340	moderate
Eco-EA	Logic-9	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1665.5	4.82e-01	1.0000000	ns	p = 1	0.0644435	small
Eco-EA	NK Landscape	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	94.0	0.00e+00	0.0000000	****	p < 1e-04	0.8174009	large
Eco-EA	NK Landscape	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	286.0	0.00e+00	0.0000000	****	p < 1e-04	0.7254073	large
Eco-EA	NK Landscape	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	528.0	0.00e+00	0.0000000	****	p < 1e-04	0.6094571	large
Eco-EA	Sorting network	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	3.0	0.00e+00	0.0000000	****	p < 1e-04	0.8610020	large
Eco-EA	Sorting network	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	69.0	0.00e+00	0.0000000	****	p < 1e-04	0.8293792	large
Eco-EA	Sorting network	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	244.0	0.00e+00	0.0000000	****	p < 1e-04	0.7455309	large
Fitness sharing	Count Odds	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	329.0	0.00e+00	0.0000000	****	p < 1e-04	0.7048046	large
Fitness sharing	Count Odds	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1742.0	7.63e-01	1.0000000	ns	p = 1	0.0277897	small
Fitness sharing	Count Odds	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2174.0	5.00e-02	1.0000000	ns	p = 1	0.1791957	small
Fitness sharing	Logic-9	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1184.0	1.24e-03	0.0744000	ns	p = 0.0744	0.2951459	small
Fitness sharing	Logic-9	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2510.0	1.96e-04	0.0117600		p = 0.01176	0.3401844	moderate
Fitness sharing	Logic-9	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2409.0	1.40e-03	0.0840000	ns	p = 0.084	0.2917920	small
Fitness sharing	NK Landscape	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	151.0	0.00e+00	0.0000000	****	p < 1e-04	0.7900903	large
Fitness sharing	NK Landscape	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	649.0	0.00e+00	0.0000001	****	p < 1e-04	0.5514821	large
Fitness sharing	NK Landscape	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	814.0	2.00e-07	0.0000139	****	p < 1e-04	0.4724251	moderate
Fitness sharing	Sorting network	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2218.0	2.84e-02	1.0000000	ns	p = 1	0.2002776	small
Fitness sharing	Sorting network	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	3335.0	0.00e+00	0.0000000	****	p < 1e-04	0.7354691	large
Fitness sharing	Sorting network	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	3084.0	0.00e+00	0.0000000	****	p < 1e-04	0.6152110	large
Lexicase	Count Odds	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	10.0	0.00e+00	0.0000000	****	p < 1e-04	0.8576480	large
Lexicase	Count Odds	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	158.0	0.00e+00	0.0000000	****	p < 1e-04	0.7867364	large
Lexicase	Count Odds	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	684.0	0.00e+00	0.0000003	****	p < 1e-04	0.5347124	large
Lexicase	Logic-9	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1057.0	9.73e-05	0.0058380	**	p = 0.005838	0.3559958	moderate
Lexicase	Logic-9	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2271.0	1.35e-02	0.8100000	ns	p = 0.81	0.2256716	small
Lexicase	Logic-9	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2658.0	6.80e-06	0.0004062	***	p = 0.0004062	0.4110990	moderate
Lexicase	NK Landscape	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1.0	0.00e+00	0.0000000	****	p < 1e-04	0.8619602	large
Lexicase	NK Landscape	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	31.0	0.00e+00	0.0000000	****	p < 1e-04	0.8475862	large
Lexicase	NK Landscape	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	188.0	0.00e+00	0.0000000	****	p < 1e-04	0.7723624	large
Lexicase	Sorting network	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	0.0	0.00e+00	0.0000000	****	p < 1e-04	0.8624394	large
Lexicase	Sorting network	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2.0	0.00e+00	0.0000000	****	p < 1e-04	0.8614811	large
Lexicase	Sorting network	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	51.0	0.00e+00	0.0000000	****	p < 1e-04	0.8380036	large
Random	Count Odds	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	503.0	0.00e+00	0.0000000	****	p < 1e-04	0.6214355	large
Random	Count Odds	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	839.0	5.00e-07	0.0000277	****	p < 1e-04	0.4604468	moderate
Random	Count Odds	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1057.0	9.73e-05	0.0058380	**	p = 0.005838	0.3559958	moderate
Random	Logic-9	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	3068.0	0.00e+00	0.0000000	****	p < 1e-04	0.6075406	large
Random	Logic-9	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1574.0	2.37e-01	1.0000000	ns	p = 1	0.1082841	small
Random	Logic-9	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	859.0	8.00e-07	0.0000478	****	p < 1e-04	0.4508641	moderate
Random	NK Landscape	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	41.0	0.00e+00	0.0000000	****	p < 1e-04	0.8427949	large
Random	NK Landscape	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	408.0	0.00e+00	0.0000000	****	p < 1e-04	0.6669531	large
Random	NK Landscape	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	801.0	2.00e-07	0.0000096	****	p < 1e-04	0.4786538	moderate
Random	Sorting network	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2374.0	2.61e-03	0.1566000	ns	p = 0.1566	0.2750223	small
Random	Sorting network	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1762.0	8.44e-01	1.0000000	ns	p = 1	0.0182071	small
Random	Sorting network	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2371.0	2.75e-03	0.1650000	ns	p = 0.165	0.2735849	small
Tournament	Count Odds	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	668.0	0.00e+00	0.0000002	****	p < 1e-04	0.5423785	large
Tournament	Count Odds	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1753.0	8.07e-01	1.0000000	ns	p = 1	0.0225193	small
Tournament	Count Odds	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1863.5	7.41e-01	1.0000000	ns	p = 1	0.0304250	small
Tournament	Logic-9	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	41.0	0.00e+00	0.0000000	****	p < 1e-04	0.8427949	large
Tournament	Logic-9	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	497.0	0.00e+00	0.0000000	****	p < 1e-04	0.6243103	large
Tournament	Logic-9	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1392.0	3.25e-02	1.0000000	ns	p = 1	0.1954863	small
Tournament	NK Landscape	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	0.0	0.00e+00	0.0000000	****	p < 1e-04	0.8624394	large
Tournament	NK Landscape	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	13.0	0.00e+00	0.0000000	****	p < 1e-04	0.8562106	large
Tournament	NK Landscape	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	59.0	0.00e+00	0.0000000	****	p < 1e-04	0.8341705	large
Tournament	Sorting network	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	9.0	0.00e+00	0.0000000	****	p < 1e-04	0.8581272	large
Tournament	Sorting network	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	30.0	0.00e+00	0.0000000	****	p < 1e-04	0.8480654	large
Tournament	Sorting network	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	210.0	0.00e+00	0.0000000	****	p < 1e-04	0.7618214	large